Question

root 2/root 5 +root 3 rationalize​

Answer 1

EXPLANATION.

$\sf \implies \displaystyle \dfrac{\sqrt{2} }{\sqrt{5} + \sqrt{3} }$

As we know that,

Rationalizes the equation, we get.

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

$\sf \implies \displaystyle \dfrac{\sqrt{2} [\sqrt{5} - \sqrt{3}] }{[(\sqrt{5})^{2} - (\sqrt{3})^{2} ]}$

$\sf \implies \displaystyle \dfrac{\sqrt{10} - \sqrt{6} }{5 - 3}$

$\sf \implies \displaystyle \dfrac{\sqrt{2} }{\sqrt{5} + \sqrt{3} } = \displaystyle \dfrac{\sqrt{10} - \sqrt{6} }{2}$

Answer 2

solution★

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

• given quantity do rationalize to we get

• $\frac{ \sqrt{2} }{ \sqrt{5} + \sqrt{3} } \times \frac{ \sqrt{5 } - \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$
• we know thAt formula of

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

• $\frac{ \sqrt{2}( \sqrt{5} - \sqrt{3}) }{( \sqrt{5}) {}^{2} - (\sqrt{3}) {}^{2} } \\ \\ \frac{ \sqrt{10} - \sqrt{6} }{5 - 3} \\ \\ \frac{ \sqrt{10} - \sqrt{6} }{2}$
• ==================================

i hope it helps you