Question

rationalize the denominator
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Answer 1

Answer:

this is ur answer

Step-by-step explanation:

mark as brilliant

Answer 2

Step-by-step explanation:

ANSWER:-

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

So,we will multiply by inverse of the denominator.

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

Now, writing the outcomes by multiplying them:-

$\dfrac{ \sqrt{7} - \sqrt{2} }{( \sqrt{7} - \sqrt{2} )( \sqrt{7} + \sqrt{2} ) }$

Now, we know the identity,

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

Using the same identity:-

$\implies \: \dfrac{ \sqrt{7} - \sqrt{2} }{ {( \sqrt{7} )}^{2} - { (\sqrt{2}) }^{2} }$

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

$\longrightarrow \: \dfrac{ \sqrt{7} - \sqrt{2} }{5}$

is the answer.

Rationalisation:-

• The process in which we simplify the denominator of a fraction is rationalization of denominator.
• In this, we multiply both with the numerator and denominator the number we obtain after investing the sign of denominator.
• The answer we obtain is the rationalized number.
• Identity generally applied is:-

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