The value of: from Quantitative Aptitude Simplification

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Simplification

Multiple Choice Questions

1.

fraction numerator left parenthesis 0.137 plus 0.098 right parenthesis squared space plus space left parenthesis 0.137 minus 0.098 right parenthesis squared over denominator 0.137 space cross times space 0.137 space plus space 0.098 space cross times space 0.098 end fraction

is simplified to

2.0
0.2
0.235
0.235

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2.

If $straight a open parentheses 2 space minus space square root of 3 close parentheses space equals space straight b space left parenthesis 2 space plus space square root of 3 right parenthesis space equals space 1 comma$ then the value of (a² - b²) is

$8 square root of 3$
$3 square root of 8$
$6 square root of 3$
$6 square root of 3$

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3.

The simplified value of $6 square root of left parenthesis 27 right parenthesis to the power of negative 2 over 3 space end exponent plus space left parenthesis 8 right parenthesis to the power of negative 2 over 3 end exponent end root$ is

$6 square root of 35$
$fraction numerator 6 over denominator square root of 13 end fraction$
$square root of 13$
$square root of 13$

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4.

fraction numerator 1 over denominator square root of 1 plus square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 begin display style plus end style begin display style square root of 3 end style end fraction plus fraction numerator 1 over denominator square root of 3 begin display style plus end style begin display style square root of 4 end style end fraction plus.... plus fraction numerator 1 over denominator square root of 99 begin display style plus end style begin display style square root of 100 end style end fraction

is equal to

$10 minus square root of 99$
$square root of 2 minus 10$
$7$
$7$

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5.

square root of 30 plus 12 square root of 6 end root space minus space square root of 4 plus 2 square root of 3 end root space minus space square root of 19 minus 6 square root of 2 end root

is simplified to

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

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6.

open square brackets left parenthesis 0.0016 right parenthesis to the power of 0.16 end exponent space cross times space left parenthesis 0.0016 right parenthesis to the power of 0.09 end exponent close square brackets

is equal to

0.2
0.4
0.16
0.16

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7.

fraction numerator 0.5 space cross times space 0.5 space cross times 0.5 space minus space 0.2 space cross times space 0.2 space cross times space 0.2 space plus space 0.3 space cross times space 0.3 space cross times space 0.3 space plus space 3 space cross times space 0.5 space cross times space 0.2 space cross times space 0.3 over denominator 0.5 space cross times space 0.5 space plus space 0.2 space cross times 0.2 space plus space 0.3 space cross times 0.3 space cross times space 0.3 space plus space 0.5 space cross times space 0.2 space plus space 0.2 space cross times space 0.3 space minus space 0.5 space cross times space 0.3 end fraction

is equal to

1
0.6
0.4
0.4

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8.
The value of:
$fraction numerator 1 over denominator square root of left parenthesis 12 minus square root of 140 right parenthesis end root end root end fraction minus fraction numerator 1 over denominator square root of left parenthesis 8 minus square root of 60 right parenthesis end root end fraction minus fraction numerator 2 over denominator square root of left parenthesis 10 plus square root of 84 right parenthesis end root end fraction$

0

1

2

2

A.

0

fraction numerator 1 over denominator square root of 12 minus square root of 140 end root end fraction space equals space fraction numerator 1 over denominator square root of 12 minus 2 square root of 5 cross times 7 end root end root end fraction space equals space fraction numerator 1 over denominator square root of 5 plus 7 space minus 2 square root of 5 cross times square root of 7 end root end fraction space equals space fraction numerator 1 over denominator square root of begin display style open parentheses square root of 7 begin display style minus end style begin display style square root of 5 end style close parentheses squared end style end root end fraction

equals space fraction numerator 1 over denominator square root of 7 minus square root of 5 end fraction space equals space fraction numerator 1 space cross times space open parentheses square root of 7 plus square root of 5 close parentheses over denominator open parentheses square root of 7 minus square root of 5 close parentheses space end fraction space equals space fraction numerator square root of 7 space plus space square root of 5 over denominator 2 end fraction

....(i)

fraction numerator 1 over denominator square root of left parenthesis 8 minus square root of 60 right parenthesis end root end fraction space equals space fraction numerator 1 over denominator square root of 8 minus 2 square root of 5 cross times square root of 3 end root end fraction space equals space fraction numerator 1 over denominator square root of 5 begin display style minus end style begin display style square root of 3 end style end fraction space equals space fraction numerator square root of 5 begin display style plus end style begin display style square root of 3 end style over denominator 2 end fraction

...(ii)

fraction numerator 2 over denominator square root of left parenthesis 10 plus square root of 84 right parenthesis end root end fraction space equals space fraction numerator 2 over denominator square root of 10 space plus 2 space cross times space square root of 7 space cross times space square root of 3 end root end fraction space equals space fraction numerator 2 over denominator square root of 7 begin display style plus end style begin display style square root of 3 end style end fraction

equals space fraction numerator 2 open parentheses square root of 7 minus square root of 3 close parentheses over denominator open parentheses square root of 7 plus square root of 3 close parentheses space open parentheses square root of 7 minus square root of 3 close parentheses end fraction equals space fraction numerator square root of 7 minus square root of 3 over denominator 2 end fraction space space space space space... left parenthesis iii right parenthesis

∴ Expression (from (i), (ii), (iii))

equals space fraction numerator square root of 7 plus square root of 5 over denominator 2 end fraction space minus space fraction numerator square root of 5 plus square root of 3 over denominator 2 end fraction space minus space fraction numerator square root of 7 minus square root of 3 over denominator 2 end fraction equals space fraction numerator square root of 7 space plus space square root of 5 minus square root of 5 space minus square root of 3 space minus square root of 7 space plus space square root of 3 over denominator 2 end fraction equals space space 0

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9.

square root of 30 plus 12 square root of 6 space end root space minus space square root of 4 plus 2 square root of 3 end root space space minus space square root of 19 space minus space 6 square root of 2 end root

is simplified to

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

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10.

open parentheses 2 minus 1 third close parentheses space open parentheses 2 minus 3 over 5 close parentheses space open parentheses 2 minus 5 over 7 close parentheses space..... space open parentheses 2 minus 997 over 999 close parentheses

is equal to

$1001 over 999$
$999 over 1001$
$1001 over 3$
$1001 over 3$

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1
2

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