Question

The value of 2/√5-+√3 is ________​

Answer 1

Answer:

answer is value is 2√5-√3/2

Answer 2

Answer:

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

Step-by-step explanation:

To find the value of $\frac{2}{\sqrt{5} - \sqrt{3} }$, we need to rationalize the denominator

The rationalizing factor is $\sqrt{5} + \sqrt{3}$

To rationalize the denominator, let us multiply and divide the given expression    $\frac{2}{\sqrt{5} - \sqrt{3} }$ with the rationalizing factor

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

apply the identity $(a+b)(a-b) = a^{2} -b^{2}$

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

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

= $\frac{2 *({\sqrt{5} + \sqrt{3})}}{2 }$

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

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

Hence, the value  of    $\frac{2}{\sqrt{5} - \sqrt{3} }$ =   $\sqrt{5} + \sqrt{3}$