Question

Rationalise the denominator of 1/√5+√2.

Answer 1

Hello Mate!

$\frac{1}{ \sqrt{5} + \sqrt{2} } \\ rationalization \\ \frac{1}{ \sqrt{5} + \sqrt{2} } \times \frac{ \sqrt{5} - \sqrt{2} }{ \sqrt{5} - \sqrt{2} } \\ \frac{ \sqrt{5} - \sqrt{2} }{5 - 2} = \frac{ \sqrt{5} - \sqrt{2} }{3}$
Hope it helps☺!

Answer 2

$\bf \frac{1}{ \sqrt{5} + \sqrt{2} } = \frac{ \sqrt{5} - \sqrt{2} }{ 3}$

Given:

• $\frac{1}{ \sqrt{5} + \sqrt{2} }$

To find:

• Rationalize the denominator.

Solution:

Concept to be used:

Rationalization: It is used to free the denominator from any radical sign.

For that, multiply and divide the fraction with RF of denominators.

• if denominator is $a + \sqrt{b}$ then, RF factor is $a - \sqrt{b}$.

Step 1:

Find the RF.

As denominator is $\sqrt{5} + \sqrt{2}$

then rationalization factor is $\bf \sqrt{5} - \sqrt{2}$

Step 2:

Multiply and divide by RF.

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

or

Apply identity

$\bf (x - y)(x + y) = {x}^{2} - {y}^{2}$

So,

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

or

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

or

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

Thus,

Rationalization of $\frac{1}{ \sqrt{5} + \sqrt{2} }$ is $\bf \frac{ \sqrt{5} - \sqrt{2} }{3}$

Learn more:

1) Rationalize the denominator

$\bf \dfrac{√6}{√3+√2}$

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2) if x = 3 + √8. find the value of x^2 + 1/x^2

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