Question

Rationalize the denominator and simplify to find the value
of : 4/√5+√3
Given that √5=2.236 and √3=1.732.​

Answer 1

Here u go ♥️♥️

Refer the attachment.

Hope it helps u............

Answer 2

The value of $\dfrac{4}{\sqrt{5}+\sqrt{3}}$ = 1.008

Step-by-step explanation:

We have,

$\dfrac{4}{\sqrt{5}+\sqrt{3}}$

To find, the value of $\dfrac{4}{\sqrt{5}+\sqrt{3}}$ = ?

∴ $\dfrac{4}{\sqrt{5}+\sqrt{3}}$

Rationalizing the denominator, we get

$=\dfrac{4}{\sqrt{5}+\sqrt{3}}\times \dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

$=\dfrac{4(\sqrt{5}-\sqrt{3})}{\sqrt{5}^2-\sqrt{3}^2}$

Using the algebraic identity,

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

$=\dfrac{4(\sqrt{5}-\sqrt{3})}{5-3}$

$=\dfrac{4(\sqrt{5}-\sqrt{3})}{2}$

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

Given by question,

$\sqrt{5}$ = 2.236 and $\sqrt{3}$ = 1.732

= 2(2.236 - 1.732)

= 2(0.504)

= 1.008

∴ The value of $\dfrac{4}{\sqrt{5}+\sqrt{3}}$ = 1.008