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# Square and Cube Roots Aptitude Multiple Choice Questions and Answers

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 6 Simplify : (  √3-(1/√3) )2 A. 3/4 B. 4/3 C. 4/√3 D. None of these
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Explanation

(  √3-(1/√3) )2

= (√3)2 +   (1/√3)2  - 2 x √3  x (1/√3)

= 3 + 1/3 -2

=1 + 1/3

=4/3

 7 If x =( √3 + 1 )/ (√3 - 1)and y =(√3 - 1)/ (√3 + 1), then the value of (x2 + y2) is: A. 10 B. 14 C. 13 D. 15
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Explanation

Let's Rationalize both x and y first,

X =( √3 + 1 )/ (√3 - 1) x ( √3 + 1 )/( √3 + 1 )

= ( √3 + 1 ) /(3-1)= (3+1+2√3  )  / 2 = 2+ √3 .

and

Y =(√3 - 1)/ (√3 + 1) x ( √3 - 1 )/( √3 - 1 )

= ( √3 - 1 )2 /(3-1)= (3+1-2√3  )  / 2 = 2- √3

So,

x2 + y2 = (2 + √3)2 + (2 - √3)2

=2 (4+ 3)

=14

 8 What should come in place of both x in the equation x / √128=√162/ x A. 12 B. 14 C. 144 D. 196
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Explanation

x / √128=√162/ x

=> x2 = √128 x 162

=>√64 x 2 x 18 x 9

=>√82 x 62 x 3 2

=> 8 x 6 x 3

=> 144

x = √144 = 12

 9 If √5 = 2.236, then the value of √5/2 -10/ √5 + √125 is equal to?? A. 5.59 B. 7.826 C. 8.994 D. 10.062
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Explanation

5/2 - 10/√5 + √125

Taking the LCM of denominators 2 and √5  = 2√5  We get,

(( √5 )- 10 x 2 +  2√5  x  5√5 ) /  2√5

= (5 - 20  + 50 ) /  2√5

Rationalizing the expression:

= 35/( 2√5 )  x √5 / √5

=35√5 /10

= (7 x 2.236) / 2

=7 x 1.118

= 7.826

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## Square and Cube Roots Aptitude Multiple Choice Questions and Answers with Explanation

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