Math, asked by bisheshsingh852, 10 months ago

Rationalize the denominator....
both..

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Answers

Answered by Anonymous

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$\huge \tt {ANSWER:}$

$\huge \tt { \frac{1}{ \sqrt{5} + \sqrt{2} } }$

$\huge \tt { = \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2}} }$

$\huge \tt { = \frac{ \sqrt{5} - \sqrt{2} }{5 - 2}}$

$\huge \tt { = \frac{ \sqrt{5} - \sqrt{2} }{3}}$

$\huge \tt { \frac{1}{ \sqrt{7} - \sqrt{2} } }$

$\huge \mathfrak { = \frac{1}{ \sqrt{7} - \sqrt{2} } \times \frac{ \sqrt{7} + \sqrt{2} }{ \sqrt{7} + \sqrt{2} } }$

$\huge \tt { = \frac{ \sqrt{7} + \sqrt{2} }{7 - 2}}$

$\huge \tt { = \frac{ \sqrt{7} + \sqrt{2} }{5} }$

HOPE IT HELPS YOU ARMY

Answered by Sudhir1188

ANSWER:

(1) (√5-√2)/3

(1) (√7+2)/3

GIVEN:

(1)

$\dfrac{1}{ \sqrt{5} + \sqrt{2} }$

(2)

$\dfrac{1}{ \sqrt{7} - 2 }$

TO FIND:

The value of the above expressions.

SOLUTION:

(1)

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

(2)

$= \dfrac{1}{ \sqrt{7} - 2 } \\ \\ = \frac{1( \sqrt{7} + 2)}{( \sqrt{7} - 2)( \sqrt{7} + 2) } \\ \\ = \frac{( \sqrt{7} + 2) }{7 - 4} \\ \\ = \frac{ \sqrt{7} + 2 }{3}$

NOTE

some important formulas:

(a+b)(a-b) = a²-b²
(a+b)² = a²+b²+2ab
(a-b)² = a²+b²-2ab

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