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Simplification

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

2.0

0.2

0.235

0.039

Solution

A.

2.0

Let 0.137 = a and 0.098 = b
∴ Expression
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$fraction numerator 1 over denominator square root of 1 plus square root of 2 end fraction plus fraction numerator 1 over denominator square root of 2 begin display style plus end style begin display style square root of 3 end style end fraction plus fraction numerator 1 over denominator square root of 3 begin display style plus end style begin display style square root of 4 end style end fraction plus.... plus fraction numerator 1 over denominator square root of 99 begin display style plus end style begin display style square root of 100 end style end fraction$ is equal to
$10 minus square root of 99$
$square root of 2 minus 10$
$7$

9

Solution

D.

9

Shorcut Method:
Subtract the highest and lowest value
$square root of 100 space minus space square root of 1 space equals space 10 space minus space 1 space equals space 9$

Question

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$square root of 30 plus 12 square root of 6 end root space minus space square root of 4 plus 2 square root of 3 end root space minus space square root of 19 minus 6 square root of 2 end root$ is simplified to
$3 square root of 2$
$square root of 2$
$2 square root of 3$
$square root of 3$

Solution

D.

square root of 3

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

0.2

0.4

0.16

1.0

Solution

A.

0.2

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$fraction numerator 0.5 space cross times space 0.5 space cross times 0.5 space minus space 0.2 space cross times space 0.2 space cross times space 0.2 space plus space 0.3 space cross times space 0.3 space cross times space 0.3 space plus space 3 space cross times space 0.5 space cross times space 0.2 space cross times space 0.3 over denominator 0.5 space cross times space 0.5 space plus space 0.2 space cross times 0.2 space plus space 0.3 space cross times 0.3 space cross times space 0.3 space plus space 0.5 space cross times space 0.2 space plus space 0.2 space cross times space 0.3 space minus space 0.5 space cross times space 0.3 end fraction$
is equal to

1

0.6

0.4

0.03

Solution

B.

0.6

Let 0.5 = a, b = -0.2 and 0.3 = c
∴ Expression
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