Question

rationalise the denominator
please give me correct answer of this question if you give correct answer I will mark you as brain list
it is very very urgent please ​

Answer 1

Question :

Rationalise the following denominator :-

$\bold\red{a) ~ \dfrac{6}{\sqrt 5 + \sqrt 2}}$

$\bold\red{b) ~ \dfrac{1}{2\sqrt 5 + \sqrt 2}}$

Solution :

Question :

$\bold\red{a) ~ \dfrac{6}{\sqrt 5 + \sqrt 2}}$

Answer →

To rationalise the denominator, we shall multiply the denominator and the numerator by (5 - √2).

$\\ \longrightarrow\quad\sf \dfrac{(6)( \sqrt{5} - \sqrt{2} ) }{(\sqrt 5 + \sqrt 2)( \sqrt{5} - \sqrt{2} )}$

Using Identity :-

• (a - b)(a + b) = a² - b²

Here,

• a = 5
• b = √2

$\\ \longrightarrow\quad\sf \dfrac{(6)( \sqrt{5} - \sqrt{2} ) }{(\sqrt 5 )^2 - (\sqrt 2)^2}$

$\\ \longrightarrow\quad\sf \dfrac{(6)( \sqrt{5} - \sqrt{2} ) }{(\sqrt 5 \times \sqrt{5} ) - (\sqrt 2 \times \sqrt{2} )}$

$\\ \longrightarrow\quad\sf \dfrac{(6)( \sqrt{5} - \sqrt{2} ) }{5 - 2}$

$\\ \longrightarrow\quad\sf \dfrac{(6)( \sqrt{5} - \sqrt{2} ) }{3}$

$\\ \longrightarrow\quad\sf \dfrac{( \not6)( \sqrt{5} - \sqrt{2} ) }{ \not3}$

$\\ \longrightarrow\quad\sf (2)( \sqrt{5} - \sqrt{2} )$

$\\ \longrightarrow\quad\sf 2\sqrt{5} - 2\sqrt{2}$

$\\ \quad\pmb{ { \blue{ \boxed{\rm \star \quad Answer \: \: \: = \: \: 2\sqrt{5} - 2\sqrt{2}}}}}$

Question :

$\bold\red{b) ~ \dfrac{1}{2\sqrt 5 + \sqrt 2}}$

Answer →

To rationalise the denominator, we shall multiply the denominator and the numerator by (2√5 - √2).

$\\ \longrightarrow \quad \sf\dfrac{(1)(2 \sqrt{5} - \sqrt{2} )}{(2\sqrt 5 + \sqrt 2)(2 \sqrt{5} - \sqrt{2} ) }$

Using Identity :-

• (a - b)(a + b) = a² - b²

Here,

• a = 2√5
• b = √2

$\\ \longrightarrow \quad \sf\dfrac{2 \sqrt{5} - \sqrt{2}}{(2\sqrt 5)^2 - ( \sqrt 2)^2 }$

$\\ \longrightarrow \quad \sf\dfrac{2 \sqrt{5} - \sqrt{2}}{(2\sqrt 5 \times 2 \sqrt{5} ) - ( \sqrt 2 \times \sqrt{2} ) }$

$\\ \longrightarrow \quad \sf\dfrac{2 \sqrt{5} - \sqrt{2}}{20- 2 }$

$\\ \longrightarrow \quad \sf\dfrac{2 \sqrt{5} - \sqrt{2}}{18 }$

$\\ \quad\pmb{ { \blue{ \boxed{ \rm\star \quad Answer \: \: \: = \: \: \frac{2 \sqrt{5} - \sqrt{2} }{18} }}}}$