Question

What is the rationalising factor of root3+root2/root3-root2 help asap! ;(

Answer 1

Question :

Rationalising factor of

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} }$

Answer :

The rationalising factor √3+√2.

Explanation :

Rationalising factor :

• If the product of two surds is a rational number, then each surd is rationalising factor to the other.

Now here,

$\frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3 } + \sqrt{2} }{ \sqrt{3} + \sqrt{2} }$

$\implies \: \frac{ { (\sqrt{3} + \sqrt{2} ) }^{2} }{ { (\sqrt{3}) - (\sqrt{2} ) }^{2} }$

$\implies \: \frac{3 + 2 + 2 \sqrt{6} }{3 - 2}$

$\implies \: \frac{5 + 2 \sqrt{6} }{1}$

$\implies \: 5 + 2 \sqrt{6}$

Here , we got a rational number.

So, it is confirmed that , √3+√2 is rationalising factor.