How To Rationalize The Denominator Of a Surd

To rationalize the denominator means to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.
When the denominator is a monomial, the basic strategy is to apply the fact that
√x * √x = (√x)² = x
On the other hand, if the denominator is a binomial, the notion of conjugate comes in handy. The conjugate of a binomial is equal to the binomial itself, however, the middle sign is changed or switched.
And so if two conjugates are multiplied together, the result is always rational.
Example (√a+√b)(√a-√b) = √a²-√b² = a-b
and a-b is rational.
While dealing with Fractions in which the denominator is an irrational, to make it rational, you need to multiply the top and the bottom by the same irrational number on the denominator for a monomial surd.
For a binomial surd, you need to multiply the top and bottom by the conjugate of the denominator.
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Пікірлер: 75

  • @ndifonchristopher7540
    @ndifonchristopher7540 Жыл бұрын

    Anyone who does not understand needs a doctor. Such an amazing teacher!!!

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you 🙏

  • @lohithsreeram3486
    @lohithsreeram34862 жыл бұрын

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  • @tambuwalmathsclass

    @tambuwalmathsclass

    2 жыл бұрын

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  • @AniConsole
    @AniConsole Жыл бұрын

    Thanks so much! This really helped me in my exam.

  • @mariamamarenah6864
    @mariamamarenah6864 Жыл бұрын

    Wow all thanks to you I never know know I will understand surds but today i really understand it well

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

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  • @BabyfaceJaiyeBear
    @BabyfaceJaiyeBear2 жыл бұрын

    You're such a great Lecturer, I should give you my tuition instead haha

  • @tambuwalmathsclass

    @tambuwalmathsclass

    2 жыл бұрын

    Thank you

  • @ngoziuruawuike6779
    @ngoziuruawuike6779 Жыл бұрын

    I understand your lesson perfectly

  • @josephfreemanattah6639
    @josephfreemanattah66392 жыл бұрын

    Many thanks for simplifying this seeming complex problem.

  • @tambuwalmathsclass

    @tambuwalmathsclass

    2 жыл бұрын

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  • @ganiuenochdiko3416
    @ganiuenochdiko34165 ай бұрын

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  • @tambuwalmathsclass

    @tambuwalmathsclass

    5 ай бұрын

    Thank you 🙏

  • @emmanuelyeanay
    @emmanuelyeanay Жыл бұрын

    Thanks for your explanation.

  • @hello4787
    @hello4787 Жыл бұрын

    Keep it up sir, love from India 🇮🇳

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you 🙏

  • @fridaynweke7060
    @fridaynweke70607 ай бұрын

    U really a good teacher sir

  • @dingdingmansagm8086
    @dingdingmansagm80866 ай бұрын

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  • @user-ib1py9ly1p
    @user-ib1py9ly1p3 ай бұрын

    You such a good teacher , Thanks a lot

  • @VsgSurya
    @VsgSuryaАй бұрын

    Keep it sir ,love from India

  • @MLBeatz023
    @MLBeatz0232 жыл бұрын

    Am able to understand everything please 🙏 we need Physics and chemistry to be explained in this slow understandable way

  • @user-if5jh9rl3w
    @user-if5jh9rl3w2 ай бұрын

    Really that's so cute and i will improve my Mathematics with you.Great thanks sir

  • @Zeiitt
    @Zeiitt Жыл бұрын

    Omor! Thank you, sir.

  • @user-oi7fr9cv9k
    @user-oi7fr9cv9k5 ай бұрын

    Thx so much, I have got it🙂

  • @moniquemichelo6504
    @moniquemichelo65045 күн бұрын

    @sir where is the _2 square 6 the 2 where is it coming from?

  • @rjshindegamerz1645
    @rjshindegamerz164527 күн бұрын

    Thank kyu so much sir ❤❤❤

  • @adamrahima8780
    @adamrahima8780 Жыл бұрын

    Thanks ❤ for helping fro🇿🇲

  • @fridaynweke7060
    @fridaynweke70607 ай бұрын

    Thanks sir

  • @dhazalletey
    @dhazalletey5 ай бұрын

    Understood 💯💯💯

  • @musonda_one7222
    @musonda_one72226 ай бұрын

    Thanks

  • @MohamudMudu-cu2kc
    @MohamudMudu-cu2kc5 ай бұрын

    Great teqc

  • @jidetoheeb4136
    @jidetoheeb41362 жыл бұрын

    I really enjoy your classes.. kudos

  • @tambuwalmathsclass

    @tambuwalmathsclass

    2 жыл бұрын

    Thank you

  • @Zeiitt
    @Zeiitt Жыл бұрын

    Learning made easy.

  • @user-kq1mh7yf8o
    @user-kq1mh7yf8o9 ай бұрын

    Thanks for helping 🥳🤣🥳🥳🔥

  • @MLBeatz023
    @MLBeatz0232 жыл бұрын

    What about functions and sketches

  • @onyibeorunoma7227
    @onyibeorunoma72272 жыл бұрын

    Please sir can you please solve this question I saw it in a jamb past question I think it's on surd. (4)√1+a - √a ÷ √1+a + √a

  • @legendboy9045
    @legendboy9045 Жыл бұрын

    Thank you so much i am Indian 🇮🇳 but you are step by step proper explain

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you 🙏

  • @tajudeennoah9948
    @tajudeennoah99483 жыл бұрын

    Wonderful approach, thanks!

  • @tambuwalmathsclass

    @tambuwalmathsclass

    3 жыл бұрын

    Thanks

  • @quinqaph5749
    @quinqaph5749 Жыл бұрын

    You are good sir...I just subscribed ❤️

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you

  • @goodnessrosemary
    @goodnessrosemary Жыл бұрын

    You're the best sir

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you 🙏

  • @7kingsand4queens_
    @7kingsand4queens_ Жыл бұрын

    You r amazing sir, love from India🇮🇳

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thanks

  • @user-ut6yt8nv9e
    @user-ut6yt8nv9e6 ай бұрын

    You are a very amazing teacher thank vlots of❤❤❤❤ 13:17

  • @user-ut6yt8nv9e

    @user-ut6yt8nv9e

    6 ай бұрын

    Thank a lot Sorry gor error

  • @user-ut6yt8nv9e

    @user-ut6yt8nv9e

    6 ай бұрын

    Sorry for error

  • @omoloyedamilola1606
    @omoloyedamilola1606 Жыл бұрын

    Cool❤

  • @nuellajae8793
    @nuellajae87932 жыл бұрын

    Simplifying surds is really difficult...pls make it easier for me

  • @AgnesKodua
    @AgnesKodua2 ай бұрын

    I understand different of two square in surds

  • @ngwadestiny8900
    @ngwadestiny8900 Жыл бұрын

    It is very very very good but sir please you can't just produce a single video for on topic complete

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    I made series of videos for every chapter, they are on my KZread playlists

  • @mayorkunayanfeolah4807
    @mayorkunayanfeolah4807 Жыл бұрын

  • @ebrimatouray1765
    @ebrimatouray17653 ай бұрын

    thank u teacher watching 2024

  • @michealotchere1229
    @michealotchere1229 Жыл бұрын

    Root 2 by Root 2should be the same number which is 2 right and not root 4 as u solved in ur second example; Pls check it for me🙏

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Root 4 is 2, recall

  • @michealotchere1229

    @michealotchere1229

    Жыл бұрын

    @@tambuwalmathsclass Tnx very much

  • @user-jw7lv3ye8v

    @user-jw7lv3ye8v

    9 ай бұрын

    Please forward the answers

  • @user-jw7lv3ye8v
    @user-jw7lv3ye8v9 ай бұрын

    √300_3√12+7√25

  • @vermaji630
    @vermaji6306 күн бұрын

    Where are you from?

  • @tambuwalmathsclass

    @tambuwalmathsclass

    5 күн бұрын

    Nigeria

  • @vermaji630

    @vermaji630

    5 күн бұрын

    @@tambuwalmathsclass I'm From India

  • @ngoziuruawuike6779
    @ngoziuruawuike6779 Жыл бұрын

    Sir you are making illustrations

  • @tambuwalmathsclass

    @tambuwalmathsclass

    Жыл бұрын

    Thank you

  • @anthonyonuchukwu4746
    @anthonyonuchukwu4746 Жыл бұрын

    Please simplify 1/(1-√3)^2

  • @monkeydflunky4788

    @monkeydflunky4788

    Жыл бұрын

    Oga go do ur assignment

  • @EbrimaOBah
    @EbrimaOBah Жыл бұрын

  • @mohamedkamara621
    @mohamedkamara621 Жыл бұрын

    X6=19x3=126

  • @mohamedkamara621

    @mohamedkamara621

    Жыл бұрын

    How to solve this equation.

  • @dicksonsunny4181
    @dicksonsunny4181 Жыл бұрын

    Interesting

  • @AgnesKodua
    @AgnesKodua2 ай бұрын

    I understand different of two square in surds