Question

Simplify :

2/√5 − √3​

Answer 1

Required Answer:-

Given To Rationalise:

• 2/(√5 - √3)

Solution:

Given,

$\sf = \dfrac{2}{ \sqrt{5} - \sqrt{3} }$

Rationalizing,...

$\sf = \dfrac{2}{ \sqrt{5} - \sqrt{3} } \times \dfrac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$\sf = \dfrac{2( \sqrt{5} + \sqrt{3})}{( \sqrt{5} - \sqrt{3})( \sqrt{5} + \sqrt{3})}$

Using identity a² - b² = (a + b)(a - b), we get,

$\sf = \dfrac{2( \sqrt{5} + \sqrt{3})}{(\sqrt{5})^{2} - (\sqrt{3})^{2}}$

$\sf = \dfrac{2( \sqrt{5} + \sqrt{3})}{5 - 3}$

$\sf = \dfrac{2( \sqrt{5} + \sqrt{3})}{2}$

Cancelling out 2, we get,

$\sf =\sqrt{5} + \sqrt{3}$

Now,

→ √5 = 2.24 and,

→ √3 = 1.73

So,

$\sf \sqrt{5} + \sqrt{3}$

$\sf =2.24 + 1.73$

$\sf = 3.97$

Answer:

• Result after simplification = 3.97.

Answer 2

Answer:

$\frac{2}{\sqrt{5} } - \sqrt{3} = \frac{2 - \sqrt{15} }{\sqrt{5} } \times \frac{ \sqrt{5} }{\sqrt{5} } = \frac{2 \sqrt{5 } - 5 \sqrt{3} }{5} .$

Step-by-step explanation:

Hope it helps.