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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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The square root of is

None of these

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7.
The value of $square root of 72 plus square root of 72 plus square root of 72 plus.......... end root end root end root$

9

8

18

18

$straight x space equals space square root of 72 plus square root of 72 plus square root of 72 plus......... end root end root end root$
S.B.S.
$straight x squared space equals space 72 space plus space square root of 72 plus square root of 72 plus square root of 72 plus........ end root end root end root$

$rightwards double arrow space space straight x squared space equals space 72 space plus space straight x rightwards double arrow space space straight x squared space minus space straight x space minus 72 space equals space 0 rightwards double arrow space straight x squared minus 9 straight x plus 8 straight x minus 72 space equals space 0 rightwards double arrow space straight x left parenthesis straight x minus 9 right parenthesis plus 8 left parenthesis straight x minus 9 right parenthesis space equals space 0 rightwards double arrow space space left parenthesis straight x plus 8 right parenthesis space left parenthesis straight x plus 9 right parenthesis space equals space 0 rightwards double arrow space space space straight x space equals space 9 space because space straight x space not equal to negative 8$

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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