Question

26. Rationalise the denominator 1/(sqrt 5 + sqrt 2)​

Answer 1

1/(√5 + √2)

1/(√5 + √2) × (√5-√2)/ (√5-√2)

(√5-√2)/ √5²-√2²

(√5-√2)/5-2

(√5-√2)/3

Answer 2

The answer is

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

GIVEN

Mathematical expression

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

TO FIND

To rational the denominator of the fraction.

SOLUTION

We can simply solve the above problem as follows;

To rational the denominator we will multiply the conjugate of √5+√2 to both denominator and numerator;

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

Applying, (a+b) (a-b) = a² - b² in the denominator;

$= \frac{ \sqrt{5} - \sqrt{2} }{ { \sqrt{5} }^{2} - { \sqrt{2} }^{2} }$

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

Therefore,

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

Hence, The answer is

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

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