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Square Roots and Cube Roots

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Question
SSCCGLENQA12042042
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fraction numerator 1 over denominator cube root of 4 plus cube root of 2 plus 1 end fraction is equal to
  • cube root of 2 plus 1
  • cube root of 2 minus 1
  • negative cube root of 2 minus 1
  • 1 minus cube root of 2

Solution

B.

cube root of 2 minus 1

Expression:
fraction numerator 1 over denominator 2 to the power of begin display style 2 over 3 end style end exponent space plus space 2 to the power of begin display style 1 third end style end exponent space plus space 1 end fraction
equals space space fraction numerator 2 to the power of begin display style 1 third end style end exponent minus 1 over denominator open parentheses 2 to the power of begin display style 1 third end style end exponent minus 1 close parentheses space space open parentheses 2 to the power of begin display style 2 over 3 end style end exponent space plus space 2 to the power of begin display style 1 third end style end exponent space plus space 1 close parentheses end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space left parenthesis straight a space minus straight b right parenthesis thin space left parenthesis straight a squared space plus space ab space plus straight b squared right parenthesis space equals space straight a cubed space minus space straight b cubed close square brackets equals space space fraction numerator 2 to the power of begin display style 1 third end style end exponent minus 1 over denominator open parentheses 2 to the power of begin display style 1 third end style end exponent close parentheses cubed minus 1 end fraction space space space space space space space space space space space space equals space 2 to the power of 1 third end exponent minus 1 space equals space cube root of 2 minus 1 space space space space space space

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Question
SSCCGLENQA12042103
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square root of 12 plus square root of 12 plus square root of 12 plus.... end root end root end root is equal to

  • 2

  • 3

  • 4

  • 6

Solution

C.

4

Shortcut Method:
Co-prime factors of 12 = (4, 3) as plus sign is followed in the question therefore, larger coprime factor i.e. 4 will be the correct answer.

Question
SSCCGLENQA12042721
Wired Faculty App

square root of 64009 is equal to

  • 352

  • 523

  • 253

  • 532

Solution

C.

253

Question
SSCCGLENQA12042938
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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 660

Solution

B.

0

2. cube root of 40 space equals space 2. space cube root of 2 space cross times space 2 space cross times space 2 space cross times space 5 end root space equals space 4 cube root of 5
4. cube root of 320
space equals space 4. space cube root of 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 2 cross times 5 end root space equals space 16. space cube root of 5
equals space 3. space cube root of 625
equals space 3. space cube root of 5 space cross times space 5 space cross times space 5 space cross times space 5 end root space equals space 15. space cube root of 5
∴   Expression 
 equals space 4. cube root of 5 space minus space 16. cube root of 5 space plus space 15. space cube root of 5 space minus space 3. cube root of 5 equals space 19. cube root of 5 space minus space 19. cube root of 5 space equals space 0
 

Question
SSCCGLENQA12043132
Wired Faculty App

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

  • 2.6

Solution

C.

1.8

Expression
  equals space cube root of left parenthesis 13.608 right parenthesis squared minus left parenthesis 13.392 right parenthesis squared end root equals space cube root of left parenthesis 13.608 plus 13.392 right parenthesis space left parenthesis 13.608 minus 13.392 right parenthesis end root equals space cube root of 27 space cross times space 0.216 end root equals cube root of fraction numerator 27 space cross times space 216 over denominator 1000 end fraction end root space equals space fraction numerator space 3 space cross times space 6 over denominator 10 end fraction space equals space 1.8

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