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Quantitative Aptitude

SQUARE ROOT AND CUBE ROOT MCQs

Square Roots, Cube Roots, Squares And Square Roots

Total Questions : 547 | Page 6 of 55 pages
Question 51.

Find the least number by which 294 must be multiplied to make it a perfect square.

  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option C. -> 6
Question 52.

  1. Find the least number by which 1470 must be divided to get a number which is a perfect square.

  1.    10
  2.    20
  3.    30
  4.    40
 Discuss Question
Answer: Option C. -> 30
Question 53.

If  \(If 5 + 2√3 = a + b√3 , then find the value of a and b .\)  =   a +  b√3   , then find the value of  a and b .

  1.    a = – 6 ,  b = – 11 
  2.    a = – 11 ,  b = – 6
  3.    a = – 6 ,  b = 11 
  4.    a = 11 ,  b = – 6
 Discuss Question
Answer: Option D. -> a = 11 ,  b = – 6
Question 54.

  1. A General wishes to draw up his 36581 soldiers in the form of a solid square. After arranging them , he found that some of them are left over . How many are left ?

  1.    90
  2.    100
  3.    110
  4.    120
 Discuss Question
Answer: Option B. -> 100
Question 55.

Evaluate     \(\sqrt[3]{\sqrt{0.000064}}\)  = ?

  1.    0.2
  2.    0.02
  3.    0.002
  4.    0.0002
 Discuss Question
Answer: Option A. -> 0.2
Question 56.

By what least number 675 be multiplied to  obtain a number which is a perfect cube ?

  1.    4
  2.    5
  3.    6
  4.    7
 Discuss Question
Answer: Option B. -> 5
Question 57.

The cube root of .000216 is:

  1.    .6
  2.    .06
  3.    77
  4.    87
 Discuss Question
Answer: Option B. -> .06

(.000216)1/3 = \(\left(\frac{216}{10^{6}}\right)^{\frac{1}{3}}\)


= \(\left(\frac{6\times6\times6}{10^{2}\times10^{2}\times10^{2}}\right)^{\frac{1}{3}}\)


=\(\frac{6}{10^{2}}\)


= \(\frac{6}{100}\)


=0.06

Question 58.

What should come in place of both x in the equation \(\frac{x}{128} = \frac{162}{x}.\)

  1.    12
  2.    14
  3.    144
  4.    196
 Discuss Question
Answer: Option A. -> 12

\(Let\frac{x}{128} = \frac{162}{x}\)


Then x2 = 128 x 162


   = 64 x 2 x 18 x 9


   = 82 x 62 x 32


= 8 x 6 x 3


   = 144.


Therefore  x = 144 = 12.


 


 


 

Question 59.

The least perfect square, which is divisible by each of 21, 36 and 66 is:

  1.    213444
  2.    214344
  3.    214434
  4.    231444
 Discuss Question
Answer: Option A. -> 213444

L.C.M. of 21, 36, 66 = 2772.


Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11


To make it a perfect square, it must be multiplied by 7 x 11.


So, required number = 22 x 32 x 72 x 112 = 213444

Question 60.

\(\sqrt{1.5625} =?\)

  1.    1.05
  2.    1.25
  3.    1.45
  4.    1.55
 Discuss Question
Answer: Option B. -> 1.25

1|1.5625( 1.25
|1
|-------
22| 56
| 44
|-------
245| 1225
| 1225
|-------
| X
|-------

Therefore \(\sqrt{1.5625} = 1.25\)

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