Question

Rationalize it
$\frac{3}{ \sqrt{5 + \sqrt{2} } }$
​

Answer 1

ANSWER:

The value of above expression = √5 - √2

GIVEN:

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

TO FIND:

The value of above expression.

SOLUTION:

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

NOTE:

• In rationalisation we have to remove the square root from the denominator.
• In order to remove the square root from the denominator we have to multiply by such a number that the square root get remove.