Question

please answer me tomorrow is my exam​

Answer 1

$\dfrac{ \sqrt{5} }{ \sqrt{3} \: - \: \sqrt{5} }$

______________ [ GIVEN ]

• We have to solve it by rationalizing.

_____________________________

→ $\dfrac{ \sqrt{5} }{ \sqrt{3} \: - \: \sqrt{5} }$

Rationalize it

→ $\dfrac{ \sqrt{5} }{ \sqrt{3} \: - \: \sqrt{5} }$ × $\dfrac{ \sqrt{3} \: + \: \sqrt{5} }{\sqrt{3} \: + \: \sqrt{5}}$

→ $\dfrac{ (\sqrt{5} )( \sqrt{3} \: + \: \sqrt{5} )}{ (\sqrt{3} \: - \: \sqrt{5})( \sqrt{3} \: + \: \sqrt{5}) }$

(a + b) (a - b) = a² - b²

→ $\dfrac{ \sqrt{15} \: + \: \sqrt{25} }{ (\sqrt{3})^{2} \: - \: (\sqrt{5})^{2} }$

→ $\dfrac{ \sqrt{15} \: + \: \sqrt{25} }{ 3 \: - \: 5 }$

→ $\dfrac{ \sqrt{15} \: + \: \sqrt{25} }{ - \: 2 }$

→ $\dfrac{ -(\sqrt{15} \: + \: \sqrt{25} )}{ 2 }$

____________________________

$\dfrac{ -(\sqrt{15} \: + \: \sqrt{25} )}{ 2 }$

_________ [ ANSWER ]

____________________________

Answer 2

Question:-

Rationalise :

$\bold{ \frac{ \sqrt{5} }{ \sqrt{3} - \sqrt{5} } }$

Solution:-

$\bold{ \frac{ \sqrt{5} }{ \sqrt{3} - \sqrt{5} } }$

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

$\bold{ = \frac{</u></strong><strong><u>\</u></strong><strong><u>s</u></strong><strong><u>q</u></strong><strong><u>r</u></strong><strong><u>t</u></strong><strong><u>{</u></strong><strong><u>5</u></strong><strong><u>}</u></strong><strong><u>( \sqrt{3} + \sqrt{5} )}{ ( \sqrt{} {3) {}^{2} - ( \sqrt{5} ) {}^{2} } }}$

$\bold{ = \frac</u></strong><strong><u>{</u></strong><strong><u> \sqrt{</u></strong><strong><u>1</u></strong><strong><u>5</u></strong><strong><u>} + \sqrt{</u></strong><strong><u>2</u></strong><strong><u>5</u></strong><strong><u>} }{3 - 5} }$

$\bold{ = \frac</u></strong><strong><u>{</u></strong><strong><u>( \sqrt{</u></strong><strong><u>1</u></strong><strong><u>5</u></strong><strong><u> } + </u></strong><strong><u>5</u></strong><strong><u>)</u></strong><strong><u>}{ - 2</u></strong><strong><u>} </u></strong><strong><u>}$

$\bold{ = \frac{-( \sqrt{15 } + 5)}{ 2} }$