Question

Find the value of 6 / root 5 + root 3 ,if root 3 =1.732 and root 5 = 2.236.

Answer 1

go through the solution given above

Answer 2

$The \quad value \quad of \quad \frac{6}{\sqrt{5}+\sqrt{3}} =1.512$

Given:

$\frac{6}{\sqrt{5}+\sqrt{3}}$

$\sqrt{3}=1.732$

$\sqrt{5}=2.236$

To find:

The value of $\frac{6}{\sqrt{5}+\sqrt{3}}$

Answer:

$\frac{6}{\sqrt{5}+\sqrt{3}}$

By taking conjugate on both side we get,

$=\frac { 6 }{ \sqrt { 5 } +\sqrt { 3 } } \quad \times \quad \frac { \sqrt { 5 } -\sqrt { 3 } }{ \sqrt { 5 } -\sqrt { 3 } }$

$=\frac{6(\sqrt{5}-\sqrt{3})}{(\sqrt{5})^{2}-(\sqrt{3})^{2}}$

$=\frac{6(\sqrt{5}-\sqrt{3})}{5-3}$

$=\frac{6(\sqrt{5}-\sqrt{3})}{2}$

By cancel the numerator and denominator we get

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

Apply the value of $\sqrt{5} \ and \ \sqrt{3}$ on the above equation.

$= 3(2.236-1.732)$

$= 3(0.504)$

$\frac{6}{\sqrt{5}+\sqrt{3}} = 1.512$