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Simplification

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Question
SSCCGLENQA12042010
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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
equals space space fraction numerator left parenthesis straight a plus straight b right parenthesis squared space plus space left parenthesis straight a minus straight b right parenthesis squared over denominator straight a squared space plus space straight b squared end fraction equals space fraction numerator 2 left parenthesis straight a squared space plus space straight b squared right parenthesis over denominator left parenthesis straight a squared space plus space straight b squared right parenthesis end fraction space equals space 2

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Question
SSCCGLENQA12042081
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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
SSCCGLENQA12042082
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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 equals space space 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 minus space square root of 19 minus 6 square root of 2 end root equals space square root of 30 plus 2 space.6 space square root of 6 end root space minus space square root of 4 space plus space 2 cross times square root of 3 cross times 1 end root space minus space square root of 19 minus 2 space cross times space 3 square root of 2 space cross times space 1 end root equals space square root of 30 space plus space 2 space cross times 3 square root of 2 space cross times space 2 square root of 3 end root space minus space square root of left parenthesis square root of 3 plus 1 right parenthesis squared end root space minus square root of left parenthesis 3 square root of 2 minus 1 right parenthesis squared end root equals space square root of left parenthesis 3 square root of 2 space plus space 2 square root of 3 right parenthesis squared end root space minus space square root of left parenthesis square root of 3 plus 1 right parenthesis squared end root space minus square root of left parenthesis 3 square root of 2 minus 1 right parenthesis squared end root equals space 3 square root of 2 space plus space 2 square root of 3 space minus space square root of 3 space minus space 1 space minus space 3 square root of 2 space plus space 1 space equals space square root of 3

Question
SSCCGLENQA12042094
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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

Expression equals space space left parenthesis 0.0016 right parenthesis to the power of 0.16 plus 0.09 end exponent space equals space left parenthesis 0.0016 right parenthesis to the power of 0.25 end exponent space equals space open parentheses open parentheses 0.2 close parentheses to the power of 4 close parentheses to the power of 1 fourth end exponent space equals space 0.2

Question
SSCCGLENQA12042096
Wired Faculty App

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
   equals space fraction numerator straight a cubed plus straight b cubed plus straight c cubed minus 3 abc over denominator straight a squared plus straight b squared plus straight c squared minus ab minus bc minus ac end fraction equals space straight a space plus space straight b space plus space straight c space equals space 0.5 space minus space 0.2 space plus space 0.3 space equals space 0.6

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