Surds and Indices - Arithmetic Aptitude Questions and Answers

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If x = 3 +2 $\sqrt{2}$ , then the value of		$\sqrt{X}$	-	1		is:
				$\sqrt{X}$

$2\sqrt{2}$

3 $\sqrt{3}$

Answer : Option B

Explanation :

$[\sqrt{x}-$ $\frac { 1 } { \sqrt{X} } )^2$ =X+ $\frac { 1 } { X } -2$

=(3+ $2\sqrt{2}$ )+ $\frac { 1 } {(3+2€‹€‹€‹€‹€‹€‹ \sqrt{2)}} -2$

=(3+ $2\sqrt{2}$ )+ $\frac { 1 } {(3+2€‹€‹€‹€‹€‹€‹ \sqrt{2)}}$ * $\frac {( 3-€‹€‹€‹€‹2 \sqrt{2})} { (3-2\sqrt{2} )} -2$

=(3+ $2\sqrt{2}$ )+(3- $2\sqrt{2}$ )-2

[ $\sqrt{X}$ - $\frac { 1 } { \sqrt{X} }$ ]=2

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