Question

Write the rationalizing factor of 1 by root 7- root 4

Answer 1

Step-by-step explanation:

Hope you liked my answer.

Pls follow me.

Have a good day.

I am an expert, so if you follow me I will always answer your question.

Answer 2

Given: $\frac{1}{\sqrt{7} \ - \ \sqrt{4} }$

To find: Rationalisation factor of the given expression

Solution:

Rationalisation factor is an irrational number that is multiplied with the given number to make it's denominator free from square roots.

Now, the rationalisation factor of $\sqrt{a} - \sqrt{b}$ will be $\sqrt{a} + \sqrt{b}$

∵ $(\sqrt{a} - \sqrt{b} )(\sqrt{a} + \sqrt{b} )= (\sqrt{a} )^{2} - (\sqrt{b} )^{2} = a - b$, which is free from roots

Similarly,

We need to multiply the numerator and denominator of the given fraction by $(\sqrt{7} + \sqrt{4})$.

∴ $\frac{1}{\sqrt{7} \ - \ \sqrt{4} } = \frac{1}{\sqrt{7} \ - \ \sqrt{4} } * \frac{\sqrt{7} \ + \ \sqrt{4}}{\sqrt{7} \ + \ \sqrt{4}} = \frac{\sqrt{7} \ + \ \sqrt{4}}{7 \ - \ 4} = \frac{\sqrt{7} \ + \ \sqrt{4}}{3}$ (the denominator is free from roots).

Hence, rationalisation factor of the given expression is  $(\sqrt{7} + \sqrt{4})$.