If x = 3 +2\sqrt 2, then find the value of (\sqrtx-1/\sqrtx).

Surds and Indices Practice Test 1

Question : 38 of 40

Marks: +1, -0

x = 3 +2√ 2

, then find the value of

(√x-1/√x)

Solution:

x = 3 +2√ 2 =2+1+2√2

=(√2+1)^2

∴√x=(√2+1)

⇒1/√x=1/{√2+1}×{√2-1}/{√2-1}

={√2-1}/1={√2-1}

Hence,

√x-1/√x

=√2+1-√2+1=2

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