Question

)

1. Rationalise the denominator of

2
________

√3 − √5​

Answer 1

Given :–

• A fraction: $\frac{2}{ \sqrt{3} - \sqrt{5} }$

Required :–

• Rationalise the denominator.

Solution :–

Given equation is,

⟹ $\frac{2}{ \sqrt{3} - \sqrt{5} }$

Now, multiply the denominator and the numerator by $\dfrac{\sqrt{3} + \sqrt{5}}{\sqrt{3} + \sqrt{5}}$

So,

⟹ $\frac{2}{ \sqrt{3} - \sqrt{5} } \times \frac{ \sqrt{3} + \sqrt{5} }{ \sqrt{3} + \sqrt{5} }$

Now, multiply the numerator to numerator and the denominator to denominator,

We know that,

[ (a + b)(a – b) = (a)² – (b)² ]

⟹ $\frac{2( \sqrt{3} + \sqrt{5} ) }{ {( \sqrt{3} )}^{2} - { (\sqrt{5}) }^{2} }$

Exponent (2) cuts the root square.

So,

⟹ $\frac{2( \sqrt{3} + \sqrt{5} ) }{3 - 5}$

Now, multiply the roots with 2, we obtain

⟹ $\frac{2 \sqrt{3} + 2 \sqrt{5} }{ - 2}$

So, the final result is :–

⟹ $\frac{2 \sqrt{3} + 2 \sqrt{5}}{ - 2}$

After rationalising the denominator we get,

–2 as a denominator.

Hence,

–2 is the rationalising of the denominator.

Answer 2

this is how to rationalise denominato