# Write the Reciprocal of 5 + √ 2 . - Mathematics

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Answer in Brief

Write the reciprocal of $5 + \sqrt{2}$.

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#### Solution

Given that,5+sqrt2 it’s reciprocal is given as

1/(5+sqrt2)

It can be simplified by rationalizing the denominator. The rationalizing factor of 5+sqrt2 is  5 - sqrt2, we will multiply numerator and denominator of the given expression 1/(5+sqrt2)by, 5-sqrt2 to get

1/(5+sqrt2) xx (5-sqrt2)/(5-sqrt2) = (5-sqrt2)/((5)^2  - (sqrt2)^2)

= (5-sqrt2) /( 25-2)

 =  (5- sqrt2 ) / 23

Hence reciprocal of the given expression is (5- sqrt2 ) / 23 .

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.3 | Q 2 | Page 16

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