# If X = 3 + 2 √ 2 ,Then Find the Value of √ X − 1 √ X . - Mathematics

If $x = 3 + 2\sqrt{2}$,then find the value of $\sqrt{x} - \frac{1}{\sqrt{x}}$.

#### Solution

Given that:.x = 3+2sqrt2 It can be written in the form (a+b)^2 = a^2 +b^2 +2ab as

sqrtx = sqrt(3+2sqrt2)

 = sqrt(2+1+2xx 1xxsqrt2)

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

  = sqrt((sqrt2+1)^2)

 = sqrt2 +1

Therefore,

1/sqrtx = 1/(sqrt2+1)

We know that rationalization factor for sqrt2+1 is  sqrt2-1  . We will multiply numerator and denominator of the given expression  1/(sqrt2+1)by, sqrt2-1,to get

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

=(sqrt2-1)/(2-1)

= sqrt2 - 1

Hence

sqrtx - 1/sqrtx = sqrt2 +1 - (sqrt2 - 1)

 = sqrt 2+1 - sqrt2 +1

 =2

Therefore, value of the given expression is 2.

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

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.3 | Q 11 | Page 16

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