# Simplify √ 3 − 2 √ 2 . - Mathematics

Simplify $\sqrt{3 - 2\sqrt{2}}$.

#### Solution

We are asked to simplifysqrt(3 - 2sqrt2) It can be written in the form (a-b)^2 = a^2 +b^2 - 2ab  as

sqrt(3-2sqrt2)  = sqrt(2 +1 - 2 xx 1 xx sqrt2)

 = sqrt((sqrt2)^2 + (1)^2 - 2xx 1xxsqrt2)

 =  sqrt((sqrt2 - 1)^2)

  = sqrt2 - 1

Hence the value of the given expression issqrt2 - 1.

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.3 | Q 10 | Page 16

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