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Square Roots and Cube Roots

Multiple Choice Questions

The difference between 777 and the nearest perfect square number is

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fraction numerator 1 over denominator cube root of 4 plus cube root of 2 plus 1 end fraction

is equal to

$cube root of 2 plus 1$
$cube root of 2 minus 1$
$negative cube root of 2 minus 1$
$negative cube root of 2 minus 1$

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square root of 12 plus square root of 12 plus square root of 12 plus.... end root end root end root

is equal to

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The smallest number to be subtracted from 4750 so as to get a perfect square number is

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If $square root of 1 plus 27 over 169 end root space equals space 1 space plus space straight x over 13 comma$ then x equals

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6.
The square root of is

None of these

None of these

Multiply numerator and denominator by 2.

$fraction numerator 2 plus square root of 3 over denominator 2 end fraction space equals space fraction numerator 2 left parenthesis 2 plus square root of 3 right parenthesis over denominator 4 end fraction$
$equals space fraction numerator 4 plus 2 square root of 3 over denominator 4 end fraction space equals space fraction numerator 3 plus 1 plus 2 square root of 3 over denominator 4 end fraction$
$equals space fraction numerator left parenthesis square root of 3 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus space 2 cross times square root of 3 space cross times space 1 over denominator space 4 end fraction equals space open parentheses fraction numerator square root of 3 plus 1 over denominator 2 end fraction close parentheses squared$
$therefore space space space square root of fraction numerator 2 plus square root of 3 over denominator 2 end fraction end root space equals space plus-or-minus fraction numerator square root of 3 plus 1 over denominator 2 end fraction$

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The value of $square root of 72 plus square root of 72 plus square root of 72 plus.......... end root end root end root$

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A General of Army wants to form a square from 36562 armies. After arrangement, he found some armies left. How many armies were left?

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square root of 64009

is equal to

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10.

The value of:
$open curly brackets fraction numerator 3 square root of 2 over denominator left parenthesis square root of 3 plus square root of 6 end fraction minus fraction numerator 4 square root of 3 over denominator left parenthesis square root of 6 plus square root of 2 right parenthesis end fraction plus fraction numerator square root of 6 over denominator left parenthesis square root of 2 plus square root of 3 right parenthesis end fraction close curly brackets$ is