Just recently found this channel. I love maths. Been retired some years now and was getting foggy.i could get the answers but couldn’t remember why. This helps to restore the rules so I can remember why I take the steps I do. Started watching as I was my grandchild with homework and asked why I did this function before that function. I couldn’t remember why, but now I can. Thank you.

By stating the answer is more than you think was misleading as most people had the answer 5 but because of your statement thought you wanted the additional -5 too. At least that's the way it was for me. I don't think I 'm alone with this thought.

The definition of the principal square root is needed to avoid the contradictions you described. The need for both +/- square roots becomes obvious when math goes beyond linear algebraic equations.

PSR = “Principle” which means it works either as a pos or a neg thus either +5^2 or -5^2 = 25

@martinwallace5734

10 ай бұрын

PRINCIPAL

@Creshex8

5 ай бұрын

You wrote the second equation wrong. Your second equation’s left hand side is equal to -25, not 25.

How do answers that are positive and negitave at the same time apply in real life? Can these relative to coordinate graphting, as in grapgting equations.?

I'd say the answer is +/- 5, but the principal root is +5. - 5 or +5 squared are each positive 25. The policy of "principal root" surely was made to discard the negative roots since they're often not of real life usefulness.

@martinwallace5734

10 ай бұрын

PRINCIPAL root

@louf7178

10 ай бұрын

@@martinwallace5734 Yeah, I was preoccupied to look it up. Thx.

@i-love-space390

10 ай бұрын

I agree completely. Every time we had an equation in algebra and we "took the square root of both sides of the equation", they always put +- on the side with the square root. Perhaps in lower math we are always expecting the "principal square root". Outside of basic math in primary school, you never have anything but equations and solving for unknowns. Obviously, in the real world, positive answers apply most of the time. But for example when you are dealing with time in physics, negative index has an actual meaning.

@jakemccoy

10 ай бұрын

The other root is certainly useful when talking about quadratic equations, waves, etc.

@jakemccoy

10 ай бұрын

@@i-love-space390In the real world, negatives are all over the like place, like in radio waves, sound waves, etc. You cannot do any engineering without accounting for the negative portion of curves.

Nicely explained this confusing topic. Thank you.😀

Best explanation thank you

The answer is 5, but 5 is not more than what I think.

@paulwhillas6494

11 ай бұрын

I was educated back in the good old days, and had my first algebra lesson when I was 13. 60 years later I still remember vividly what happened. I successfully solved my first equation and discovered that x equalled 7. However, I then got all the following questions wrong. The teacher came over to see where I was going wrong. " I don't know." I replied. "I know that x equals seven, but when I substitute 7 for x, I get the wrong answer." Being a strong language student, I had been trying to decode what each alphabetical symbol represented, in numerical terms. I thought that each letter had a fixed value. Eventually I went on to do quite well at Double maths at university entrance level, ranking in the top 20% of students in the state. However, I never developed a love of Mathematics, and went on to be an English, Humanities, and Social sciences teacher . I loved that and was quite good at it. However, senior high school maths, and university statistics classes, gave me a useful working knowledge of mathematics

@alikhat1647

10 ай бұрын

Wait…what did your teacher not explain that left you thinking a variable (x) could be a constant number?

@MrMousley

9 ай бұрын

Yes ... but the answer could also also be -5

@Mimibryant0123

2 ай бұрын

That’s all I think…5

After some research into different sources, (of which some go one way, and some another) my conclusion is that there is no absolute authority to say when only the "principal square root" applies, and when it does not. Can you cite such an authority? If not, I will continue to use both + and - as correct, and not just the "principal square roor".

@keninnewmexico8763

9 ай бұрын

And that would be a smart way to go. I've also taught high school math for decades, and I'm all, "wtf is he going on about?" There's number theory, which is a 500 level, post-grad uni course where this comes up, and there are semester finals and SATs where +/- 5 better be your answer. I've watched 4 of this guy's vids, and every single one had what I'd call misinformation. I'm wondering if this is some weird math troll.

@gavindeane3670

2 ай бұрын

What authority definitively says that the + symbol means addition? How about the agreed international standard for mathematical notation in ISO 80000-2. That ought to be good enough for you. That's kind of the point of writing these things down in a standard - so we all know what they mean. If you want the principal square root of 25 you write √25. If you want the other square root of 25 you write -√25. If you want both square roots of 25 you write ±√25. The √ would be pretty useless if it wasn't precisely defined like that. We wouldn't be able to use it to communicate at all.

Maybe explain what quadratic is? What makes an equation quadratic?

@leohines8483

10 ай бұрын

Quadratic is: AX^2+Bx+C=0 or -b+/-√b^2-4ac/2a x^2-5x-7=0 -(-5)±√(-5)^2-4*(1-7)/2*1 5/5±√25+28/2 or 5/2 ±√53/2 x^2 -5x-7=0+7 x^2-5x=7 complete the square b/2 then, square the fraction (-5/2)^2=25/4, then add this new improper fraction to both sides, like so... x^2-5x+25/4=7+25/4 after completing the square, then factor the square and then make it into a square binomial in (x-52/2)^2 Then, make the right side agree with like denominators/least common denominator/Multiple; here, 7 is understood to be written over 1. (x-5/2)^2=28/4+25/4 or √(x-5/2)^2=±√53/√4 simplify both sides x-5/2=±√53/2... then, isolate the variable (x) on the left side of the equation, and whatever you do on one side, you do to the other. x+5/2=±√53/2+5/2=x or {5/2-√53/2 & 5/2+√53/2}

@Betelgeusewaitforit

10 ай бұрын

It's nuts, I had me fair share of quadratic equations... you can get 2 answers and then just logically prefer one with a reason. Trust me it's stupid to common sense and useful in special cases.

I think the differentiation comes in as equations vs. functions. Feels like this is an inflection point between algebra and analysis. I may be wrong, but it it feels like some fundamentals are coming into play that I will for sure not start to discuss on this vid 🙃 my student answer would have been +/- 5, for better or worse 🤓

@jakemccoy

10 ай бұрын

The answer is +/-5 when dealing with quadratic equations.

@robertstacey1700

5 ай бұрын

It is just strange to think that a number can have both a + and - value at the same time. I mean how would an answer such as +/-5 even apply in today's occupations when usually you need a specific value for something?

@gavindeane3670

2 ай бұрын

​@@jakemccoyThe answer is not ±5 when dealing with quadratic equations. The formula for solving a quadratic equation uses ±√(b²-4ac) precisely BECAUSE √(b²-4ac) is only the principal square root whereas the formula needs both square roots.

@jakemccoy

2 ай бұрын

@@gavindeane3670 See 5:15. You said the answer in quadratics is not +/- and then proceeded to explain why the answer is +/-. You are an example of why young students on the fringe lose interest in math. Congrats.

Negative numbers can be expanded to -1*N which is no longer just a simple number. So -5 squared is -1 * 5 * -1 * 5. Thus five is still the root, it loses its -1 attachment as those cancel out (which is why squares of negative numbers become the same as positive).

@gavindeane3670

2 ай бұрын

What do you mean? 25 has two square roots. They are 5 and -5. The notation √25 refers to the principal square root of 25, which is 5.

5

5 absolutely

Everything you say around 6:40 contradicts your assertion that the sqrt is just positive. I think you're being quite misleading

This is like pulling down your pants to pull up your socks .

By ''more than you think'' I assume you mean + or - 5 because both 5 x 5 and -5 x -5 = 25

Homeschooling dad subscribed😅

This video is more accurate since we defined a positive number and its square root is not showing a - sign. That is, many people working equations are choosing the positive of the choices using no sign such as + sign that could have been used to make clearer. In distance and orientation mathematics such as direction it is easier to just assume a negative value of the square root of a quadratic equations. An example is distance, of how many miles did the plane move North East flying 700 mph in a time t vs what negative miles did he go in the 180 degrees phase direction of South West at 700 mph in a time t.

The answer is 5 and it took less than a second - we used to be able to do that so easily when I was in school and we most certainly did not need to through a pointless extra process using algebra to do it.

Matrices?

67.5

👍

You mention your collection of books, so I will tell you one of my favourite books on math. 200% Of Nothing by AK Dewdney. Check it out, you'll probably like it.

@Dani-ICU-RN

11 ай бұрын

@Geoff_G " my favorite book on math.." there's a sentence I'll Never Say😅😅.. although Math and Science are my favorite and I've been in ICU RN for 23 years I feel like if you don't use it you lose it but I did get all these answers right LOL. Excuse me ,I got them correct

12.5

All numbers are a concept, they don’t exist. You may have 5 bananas, you have bananas but you don’t actually have 5.

@joluju2375

Ай бұрын

Give me five !

12.5?

I did wrong but not as shown in the video: 3(5+20/2*5) 3*(25/2*5) 3*(25/10) 3*(2,5) 3*2,5 =7,5 I thought I remembered the rules correctly... but nope!

it 5

+5, -5

The square root of x^2 is not x. It is +_x depending on x itself. For example if x=-3 then x^2=9 so that square root of x^2 is 3. But 3 is not equal to x since x=-3. Hence square root of x^2 in this -x. The square root of x^2 is +-x depending on whether x is positive or negative. The square root of a positive number is always positive

@Dani-ICU-RN

11 ай бұрын

@rogerwarren translate to English. Haaaa jkjk😅

I love your channel! Aside from some of the insufferable commenters…

5 will do just fine for me.

5,-5

Is the new math being taught accurate? It goes against everything taught prior to 2000

5.....what number times itself will give you 25.

What is the square root of a negative number?

@paulswift4562

9 ай бұрын

Square root of -1 is called i (for imaginary number) hence square root of -4 is 2i.

5 despite the gaslighting 🙂

There is one…there are two. Correct English helps covey the lesson without distractions.

@briancarter8028

10 ай бұрын

Correct English helps "covey" the lesson???

@christopherrobertson7723

10 ай бұрын

@@briancarter8028 convey

@christopherrobertson7723

10 ай бұрын

@@briancarter8028 Thank-you for the constructive criticism.

It's 5

If we were just using it in a linear equation and not a quadratic or higher, the principle square root is 5. In a quadratic equation or a polynomial equation with higher powers, it is most likely ±5.

Twins

In the solution to this problem you make the statement “the square root of x^2 is x” which is not a true statement. For example, if x = -5 then x^2 = 25. The square root of x^2 would be the square root of 25 which is 5. HOWEVER 5 does NOT equal x since x = - 5. In this case the square root of x^2 is -x which is -(-x) =-(-5) = 5. In this case -x is positive!!!

He changes the equation to make his explanation work. Genius.

@i-love-space390

10 ай бұрын

I agree. The original problem was Sqr(25) = ?, NOT Sqr(25) = 5.

All this verbiage but WHY is the principal square root the ONLY square root?

@joluju2375

9 ай бұрын

I agree this is verbiage. There is no such thing as the "principal" square root. There is only a function named "square root", and since it is a function, by definition of a function it can only have one result, as all functions do.

It's 5. Five fives are twenty five.

+/- 5 what is the square root of -25. Its an imaginary number

If positive 5 identifies itself as negative 5 then there is no correct answer. Game over.

I'm glad this guy isn't my teacher. He just wasted over 12 minutes of my time waffling, saying the same thing over and over, and still getting it wrong.

@SpideyVids

26 күн бұрын

Definitely - I literally would have learned nothing in his class.

Square root of 25 is 5. 5squared is 25

12:05 Just call this an arbitrary math rule that students need to remember. Then there is no need to understand the logic.

5 and also -5. Both are correct.

Yea, but if you change the =5 to =-5 then suddenly -5 is the only correct answer. Your point doesn't hold up mathematically, if what you were saying was true, =-5 would have a different square root then the square root of 25, which is not the case.

That's easy the square root of 25 is 5

The square root of 64 is 8, it's the number times itself

-5, +5

Simply stating 5 is not equal to -5 doesn't make -5 the wrong answer. It's still the other answer. The quadratic equation staes there are 2 answers. Under what circumstances does it not apply?

@solesurvivor5702

9 ай бұрын

*states

@gavindeane3670

2 ай бұрын

-5 is the wrong answer because the √ symbol means "principal square root of". If he had just stated that fact, the video would have been much more sensible. Instead, he launched into a completely misconceived and nonsensical attempt to try and prove why √25 is not -5.

Still didn't sort out why you should answer with only the principal root. You don't cite any authority. So you then justify (starting at 8:20 of the video) with the equation rootx=5 and then "prove" it can only be the one answer. so then could one not use the exact same reasoning to to say it MUST be -5 if they use the equation rootx=-5? So the correct answer to root 25 is positive OR negative 5

@gavindeane3670

2 ай бұрын

His "proof" at 8:20 is complete nonsense. As you've noticed, it would be just as easy to "prove" that √25 is -5. √25 is 5 and it is not -5. But that's not a thing you can prove, it's just what the symbols mean. Asking someone to prove why the √ symbol means principal square root is like asking them to prove why the + symbol means addition. It's useful in mathematical notation to be able to indicate addition, and it's useful to be able to indicate square root, so humanity has picked some symbols to indicate those things. But of course you can indicate the other square root too. Or both at the same time. If x is a positive number then x has two square roots. One of the square roots is positive (the principal square root) and it's written as √x The other square root is negative and is written as -√x If you want to refer to both square roots at the same time (for example, in the formula for solving a quadratic equation) then you write ±√x

The square root of 25 is 5

+- 5

+/- 5

The answer is NOT more than I think, which is FIVE. Don't complicate simple things!

@joluju2375

9 ай бұрын

What if I thought of 4.9 ? :D

Root within same sign ( _, +) still same but with different sign ( -) ( +) are different within same value Who explore imaginary Roots and how he prove it ???? All numbers had value within different sign. ....??? How to represent imaginary numbers ON Number line ?? Will stay on Negative side of zero ....???!....!!!!

Now, what is ✓-4 ?

@discobear5752

11 ай бұрын

✓-4 is 2i where i is the complex number ✓-1.

@luillierstephane1463

11 ай бұрын

@@discobear5752 Actually, 2I IS the complex number. 2 is the real part of it, and I is the imaginary part.

@lawrencejelsma8118

11 ай бұрын

The imaginary result is +/- 2i because [(-2)(i)][(-2)(i)] also equals [(2)(i)][(2)(i)]. The correctness is to not leave something in a square root form for clarity such as saying 2i vs square root of -4. Better yet +2i is a better way vs 2i which is okay without the + sign with no further square root symbol showing.

@Dani-ICU-RN

11 ай бұрын

You,Sir Lawrence, have Super Powers 😅🤭😉

@louf7178

10 ай бұрын

Null set, unless you want to include an imaginary patch.

The answer is + or - 5

I would also just point out that there is no square root of a negative number. Any negative number multiplied by itself is a positive number.

@TheloniousCube

10 ай бұрын

Complex numbers are a thing

@louf7178

10 ай бұрын

@@TheloniousCube Are they? Always seemed like a "work around" of wishful thinking.

@TheloniousCube

10 ай бұрын

@@louf7178 They are. Just as "real" as any other numbers. Perhaps surprisingly, they have numerous real-world applications - look it up

@BartBuzz

8 ай бұрын

The Sqrt(-25) = 5i since i^2 = -1 in the complex domain.

Nah, you can't fool me. -5 times -5 is 25. End of story.

wasted 12 minutes not really explaining where -5 fits into this example.

The answer is literally 5. What a joke of a video

Why complecate this so much ? Put a sign on that 25. It's an incomplete question without that. There is so much assumption in arithmetic it really made my school life hell. I can understand so much advanced mathematics well. This kinda nonsense just puts me off. Okay why not discuss the same with partitions, it's possible right. It sucks

This video is enough to make sure I never watch another one by this guy.

@janeoleary8454

11 ай бұрын

Good riddance

Why you making mathematics theoretical...the answer is 5 FULLSTOP😂 Now what's +/-5😒😂😒

@louf7178

10 ай бұрын

Thus the reason for the "principle root" because there ARE two solutions.

±5

plus or minus 5

answer is: (+5) and (-5).

-5,5

The square root of 25 is 5. 5x5=25. Any other answer you give is going to earn you a DISLIKE thumb down.

The answer is +5 or -5 unless you declare beforehand that you only want the positive root or principal square root ..... This guy in my opinion is a second-rate mathematician, and a poor teacher !

@gavindeane3670

2 ай бұрын

He did declare beforehand that he only wanted the principal square root. That's what the √ symbol means.

𝑎=𝑏√=−𝑎 would therefore imply that 𝑎=−𝑎

Sq root of 25 = ? is NOT 5. The Answer is -+/-5.When you changed the equation and said sq root 25 = 5, in that case the it's 5. I do not have the ability to write equations the proper way here, so bare with me. But if you are teaching your students that it is acceptable to say to the original equation is only 5, than this is why the USA sucks at math because they are being taught wrongly. Because for the equation Sq root of 25 = ? the ONLY correct answer is +/-5. And my math credentials are at least equal yours, so I know what I am talking about

5

+/- 5

-5, +5

+5, - 5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5