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Square Roots and Cube Roots

Multiple Choice Questions

31.

By what least number should 675 be multiplied so as to obtain a perfect cube number?

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32.

The square root of 0.09 is

0.30
0.03
0.81
0.081

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33.

$cube root of 1 minus 127 over 343 end root$ is equal to

$5 over 9$
$1 minus 1 over 7$
$4 over 7$
$1 minus 2 over 7$

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34.

The square root of $open parentheses fraction numerator square root of 3 space plus space square root of 2 over denominator square root of 3 space minus space square root of 2 end fraction close parentheses$ is

$square root of 3 space plus space square root of 2$
$square root of 3 space minus space square root of 2$
$square root of 2 space plus-or-minus space square root of 3$
$square root of 2 minus square root of 3$

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35.

The value of
$fraction numerator 3 square root of 2 over denominator square root of 3 space plus space square root of 6 end fraction space minus space fraction numerator 4 square root of 3 over denominator square root of 6 space end root begin display style plus end style begin display style square root of 2 end style end fraction space plus space fraction numerator square root of 6 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 2 end style end fraction$ is

4
0
$square root of 2$
$3 square root of 6$

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36.

$square root of 6 plus square root of 6 plus square root of 6 plus... end root end root end root space equals space ?$

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37.

If $square root of 2 space equals space 1.4142 comma$ find the value of $2 square root of 2 space plus space square root of 2 space plus space fraction numerator 1 over denominator 2 plus square root of 2 end fraction space plus space fraction numerator 1 over denominator square root of 2 minus 2 end fraction$

1.4144
2.8284
28.284
2.4142

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38.

If $straight x space equals space square root of fraction numerator square root of 5 space plus space 1 over denominator square root of 5 minus 1 end fraction end root space then comma$ the value of 5x² - 5x - 1 is

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39.

If $square root of 1 plus straight x over 961 end root space equals space 32 over 31$ , then the value of x is

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40.
The simplest value of $fraction numerator 1 over denominator square root of 2 space plus space square root of 3 end fraction space plus space fraction numerator 1 over denominator square root of 3 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 4 end style end fraction space plus space fraction numerator 1 over denominator square root of 4 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 5 end style end fraction space plus space fraction numerator 1 over denominator square root of 5 begin display style space end style begin display style plus end style begin display style space end style begin display style square root of 6 end style end fraction$ is

$square root of 3 space left parenthesis square root of 2 minus 1 right parenthesis$

$square root of 2 left parenthesis square root of 3 minus 1 right parenthesis$

$square root of 3 minus 1$

$square root of 2 minus 1$

$square root of 2 left parenthesis square root of 3 minus 1 right parenthesis$

Shortcut Method:
Subtract square root of smaller number from square root of larger number
$space straight i. straight e. space space square root of 6 space minus space square root of 2 space equals space square root of 2 left parenthesis square root of 3 minus 1 right parenthesis$

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Multiple Choice Questions

40. The simplest value of is