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Square Roots and Cube Roots

Multiple Choice Questions

11.

Given that $square root of 4096 space equals space 64 comma$ the value of $square root of 4096 space plus space square root of 40.96 end root space plus space square root of 0.004096 end root$ is

70.4
70.464
71.104
71.104

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12.

The square root of:
$fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator 1 minus 0.75 end fraction space plus space left square bracket 0.75 space plus space left parenthesis 0.75 right parenthesis squared plus 1 right square bracket$ is

1
2
3
3

143 Views

13.

2 cube root of 40 space minus space 4 cube root of 320 space plus space 3 cube root of 625 space minus space 3 cube root of 5

is equal to

$negative 2 cube root of 340$
0
$cube root of 340$
$cube root of 340$

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14.

The square root of
$fraction numerator left parenthesis 0.75 right parenthesis cubed over denominator 1 minus 0.75 end fraction space plus space open square brackets 0.75 space plus space left parenthesis 0.75 right parenthesis squared space plus space 1 close square brackets$ is

1
2
3
3

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15.

The square root of
$fraction numerator 9.5 space cross times space 0.0085 space cross times space 18.9 over denominator 0.0017 space cross times space 1.9 space cross times 2.1 end fraction$ is

15
45
75
75

127 Views

16.

A General, while arranging his men, who were 6000 in number, in the form of a square, found that there were 71 men left over. How many were arranged in each row?

73
77
87
87

723 Views

17.

The largest among the numbers
$square root of 7 minus square root of 5 comma$ $square root of 5 minus square root of 3 comma space$ $square root of 9 minus square root of 7 comma$ $square root of 11 minus square root of 9$

$square root of 7 minus square root of 5$
$square root of 5 minus square root of 3$
$square root of 9 minus square root of 7$
$square root of 9 minus square root of 7$

165 Views

18.

cube root of left parenthesis 13.608 right parenthesis squared space minus space left parenthesis 13.392 right parenthesis squared end root

is equal to

0.6
0.06
1.8
1.8

126 Views

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19.

fraction numerator square root of 7 over denominator square root of 16 plus 6 square root of 7 end root minus square root of 16 minus 6 square root of 7 end root end fraction

is equal

$1 half$
$1 third$
$1 fourth$
$1 fourth$

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20. $fraction numerator 6 squared plus 7 squared plus 8 squared plus 9 squared plus 10 squared over denominator square root of 7 plus 4 square root of 3 end root minus space square root of 4 plus 2 square root of 3 end root end fraction$ is equal to

330

305

355

355

A.

330

square root of 7 plus 4 square root of 3 end root space equals space square root of 7 plus 2 cross times 2 cross times square root of 3 end root space equals space square root of 4 plus 3 plus 2 cross times 2 cross times square root of 3 end root space space space space space space space space space space space space space space space space space space space space space space equals space square root of left parenthesis 2 plus square root of 3 right parenthesis squared end root space equals space space 2 space plus space square root of 3 space space space space

square root of 4 plus 2 square root of 3 end root space equals space square root of 4 plus 2 cross times square root of 3 space cross times 1 end root space equals space square root of 3 plus 1 plus 2 cross times square root of 3 cross times 1 end root

equals space square root of left parenthesis square root of 3 plus 1 right parenthesis squared end root space equals space square root of 3 space plus 1

therefore space space space space square root of 7 plus 4 square root of 3 end root space minus space square root of 4 plus 2 square root of 3 end root space equals space 2 space plus space square root of 3 space minus space square root of 3 space minus space 1 space equals space 1

Now,

1 squared space plus space 2 squared space plus space...... plus 10 squared

equals space fraction numerator 10 space left parenthesis 10 plus 1 right parenthesis thin space left parenthesis 20 plus 1 right parenthesis over denominator 6 end fraction equals space fraction numerator 10 space cross times space 11 space cross times space 21 over denominator 6 end fraction space equals space 385

1 squared plus space 2 squared space plus space. space... plus 5 squared equals space fraction numerator 5 left parenthesis 5 plus 1 right parenthesis thin space left parenthesis 10 plus 1 right parenthesis over denominator 6 end fraction equals space fraction numerator 5 space cross times space 6 space cross times space 11 over denominator 6 end fraction space equals space 55

open square brackets because space space 1 squared space plus space 2 squared space plus space 3 squared space plus space.... plus straight n squared space equals space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis thin space left parenthesis 2 straight n plus 1 right parenthesis over denominator 6 end fraction close square brackets therefore space space 6 squared plus 7 squared plus 8 squared plus 9 squared plus 10 squared space equals space 385 minus space 55 space equals space 330

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1
2
3

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