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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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2. $fraction numerator 1 over denominator cube root of 4 plus cube root of 2 plus 1 end fraction$ is equal to
$cube root of 2 plus 1$
$cube root of 2 minus 1$
$negative cube root of 2 minus 1$
$negative cube root of 2 minus 1$

cube root of 2 minus 1

Expression:
$fraction numerator 1 over denominator 2 to the power of begin display style 2 over 3 end style end exponent space plus space 2 to the power of begin display style 1 third end style end exponent space plus space 1 end fraction$

$equals space space fraction numerator 2 to the power of begin display style 1 third end style end exponent minus 1 over denominator open parentheses 2 to the power of begin display style 1 third end style end exponent minus 1 close parentheses space space open parentheses 2 to the power of begin display style 2 over 3 end style end exponent space plus space 2 to the power of begin display style 1 third end style end exponent space plus space 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space left parenthesis straight a space minus straight b right parenthesis thin space left parenthesis straight a squared space plus space ab space plus straight b squared right parenthesis space equals space straight a cubed space minus space straight b cubed close square brackets equals space space fraction numerator 2 to the power of begin display style 1 third end style end exponent minus 1 over denominator open parentheses 2 to the power of begin display style 1 third end style end exponent close parentheses cubed minus 1 end fraction space space space space space space space space space space space space equals space 2 to the power of 1 third end exponent minus 1 space equals space cube root of 2 minus 1 space space space space space space$

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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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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