Question

1/root 5 + root 3 rationalise it

Answer 1

Answer:-

$\leadsto\tt{\dfrac{1}{\sqrt{5}}+\sqrt{3}}$

By LCM,

$\leadsto\tt{\dfrac{1}{\sqrt{5}}+\dfrac{\sqrt{3}}{1}}$

$\leadsto\tt{\dfrac{1 + \sqrt{15}}{\sqrt{5}}}$

Rationalising,

$\leadsto\tt{\dfrac{1 + \sqrt{15}}{\sqrt{5}}\times \dfrac{\sqrt{5}}{\sqrt{5}}}$

$\leadsto\tt{\dfrac{1 + \sqrt{5\times3\times5}}{5}}$

Simplifying,

$\leadsto\tt{\bf{\dfrac{1 + 5\sqrt{3}}{5}}}$

$\rule{200}2$

Rationalisation is converting an irrational denominator to rational denominator in a fraction.

It helps to compute between rational denominators rather than the irrational denominators.

$\rule{200}2$

Answer 2

Step-by-step explanation:

$\frac{1}{ \sqrt{5} + \sqrt{3} } = \frac{ \sqrt{5} - \sqrt{3} }{( \sqrt{5} + \sqrt{3} )( \sqrt{5} - \sqrt{3} )} \\ = \frac{ \sqrt{5} - \sqrt{3} }{ { \sqrt{5} }^{2} - { \sqrt{3} }^{2} } = \frac{ \sqrt{5} - \sqrt{3} }{5 - 3} \\ = \frac{ \sqrt{5} - \sqrt{3} }{2}$

$<font color=blue><marquee behavior=alternate><b>PEASE MARK BRAINLIEST</b></font></marquee>$