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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?

64 Views

32.

The square root of 0.09 is

0.30
0.03
0.81
0.081

69 Views

33.

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

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

34 Views

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
$square root of 2$
$3 square root of 6$

33 Views

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

34 Views

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

0

3

4

5

$straight x space equals space square root of fraction numerator square root of 5 plus 1 over denominator square root of 5 minus 1 end fraction space cross times space open parentheses fraction numerator square root of 5 plus 1 over denominator square root of 5 plus 1 end fraction close parentheses end root equals space square root of fraction numerator left parenthesis square root of 5 plus 1 right parenthesis squared over denominator 5 minus 1 end fraction end root space equals space square root of fraction numerator left parenthesis square root of 5 plus 1 right parenthesis squared over denominator 4 end fraction end root equals space fraction numerator square root of 5 plus 1 over denominator 2 end fraction$
∴ 5x² - 5x - 1
$equals space 5 open parentheses fraction numerator square root of 5 plus 1 over denominator 2 end fraction close parentheses squared space minus space 5 open parentheses fraction numerator square root of 5 plus 1 over denominator 2 end fraction close parentheses minus 1 equals space 5 open parentheses fraction numerator 5 plus 1 plus 2 square root of 5 over denominator 4 end fraction close parentheses space minus space open parentheses fraction numerator 5 square root of 2 plus 5 over denominator 2 end fraction close parentheses minus 1 equals space 5 open parentheses fraction numerator 3 plus square root of 5 over denominator 2 end fraction close parentheses space minus space open parentheses fraction numerator 5 square root of 5 plus 5 over denominator 2 end fraction close parentheses minus 1 equals space fraction numerator 15 plus 5 square root of 5 minus 5 square root of 5 minus 5 minus 2 over denominator 2 end fraction space equals space 8 over 2 space equals space 4$

34 Views

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

31 Views

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

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