Question

write the rationlize factor of 1 upon root7 - root4\

Answer 1

Question :

• $\sf To \; rationalise \; \dfrac{1}{\sqrt7-\sqrt4}$

Solution:

Rationalising :

• To rationalise a factor we have to multiply and divide the factor by conjugate of its denominator.

Conjugate:

• To find conjugate we just have to change the sign. Example, Conjugate of a-b is a+b .

Here , we have , $\sf \dfrac{1}{\sqrt7-\sqrt4}$

So, Conjugate of $\sqrt7-\sqrt4 \sf\; will\; be \;\bf \sqrt7+\sqrt4$

Now,

$\sf\longmapsto \dfrac{1}{\sqrt7-\sqrt4} \\\\\\\sf\dasharrow \dfrac{1}{\sqrt7-\sqrt4}\times \dfrac{\sqrt7+\sqrt4}{\sqrt7+\sqrt4}\\\\\\\sf\dasharrow \dfrac{\sqrt7+\sqrt4}{\sqrt7^2-\sqrt4^2}\\\\\\\sf\dasharrow \dfrac{\sqrt7+\sqrt4}{7-4}\\\\\\\sf\dasharrow \dfrac{\sqrt7+\sqrt4}{3}$

Therefore,

• $\sf\dfrac{\sqrt7+\sqrt4}{3} \;is\; answer$

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Formulas Used :

• $\sf (a+b)(a-b)=a^2-b^2$
• $\sqrt{a}^2 = a$