Question

rationalise the denominator of 2 by √5+√3​

Answer 1

Step-by-step explanation:

2/(√5 + √3) × (√5 - √3)/(√5 - √3)

2(√5 - √3)/(√5)² - (√3)²

2√5 - 2√3/2

I hope it will help you.

Answer 2

Given: An expression $\frac{2}{\sqrt{5} \ + \ \sqrt{3} }$

To find: Rationalised form of the denominator

Solution:

The given expression is $\frac{2}{\sqrt{5} \ + \ \sqrt{3} }$

We know that $(\sqrt{a} \ + \ \sqrt{b})(\sqrt{a} \ - \ \sqrt{b}) = a -b$

∴ $(\sqrt{5} \ + \ \sqrt{3} )(\sqrt{5} \ - \ \sqrt{3} ) = 5 - 3 = 2$, which is a rational number

So, we need to multiply the numerator and denominator of the given expression by $(\sqrt{5} \ - \ \sqrt{3})$

⇒ $\frac{2}{\sqrt{5} \ + \ \sqrt{3} } = \frac{2}{\sqrt{5} \ + \ \sqrt{3} } \ * \ \frac{\sqrt{5} \ - \ \sqrt{3} }{\sqrt{5} \ - \ \sqrt{3} }$

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

⇒ $\frac{2(\sqrt{5} \ - \ \sqrt{3} \ ) }{5 \ - \ 3} = \frac{2(\sqrt{5} \ - \ \sqrt{3} \ )}{2}$

⇒ $\sqrt{5} \ - \ \sqrt{3}$

Hence, after rationalising the denominator, the expression becomes $\sqrt{5} \ - \ \sqrt{3}$