Square and Cube Root- Aptitude Questions and Answers

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What is the smallest number by which 3087 must be divided so that the quotient is a perfect cube?

A)

3


B)

21


C)

7


D)

9



Correct Answer :

9


Explanation :

Factors of 3087
3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73

here only 3 is not in the cube.

Therefore 3 is the only number that is multiplied to make it a perfect cube.
And divide it by 3 × 3 which is 9 to make it a perfect cube.

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Find the least number which when multiplied with 74088 will make it a perfect square ?

A)
42

B)
44

C)
46

D)
48


Correct Answer :

42


Explanation :

74088 = 2 * 2 * 2 * 3 * 3 * 3 * 7 * 7 * 7
= (2*2) * (3*3) * (7*7) * (2*3*7)
Least number which should be multiplied to 74088 to make it a Perfect square = 2 * 3 * 7 = 42

Find the least number by which 175760 be devided to make it a perfect cube ?

A)
10

B)
20

C)
100

D)
5


Correct Answer :

10


Explanation :

175760 = 24 x 5 x 13 3
= 23 x 2 x 5 x 133
To make perfect cube, it must be divided by 2 x 5 = 10

√(248 + √(52+ √144)) = ?

A)
14

B)
16

C)
16.6

D)
18.8


Correct Answer :

16


Explanation :

√(248 + √(52 + √144))
=> √(248 + √(52 + 12))
=> √(248 + √64)
=> √(248 + 8)
=> √256
=> 16

250 / √? = 10

A)
25

B)
250

C)
625

D)
2500


Correct Answer :

625


Explanation :

Let 250 / √x = 10.
Then √x= 250 / 10 = 25
Thus, x = 625

√(4/3) - √(3/4) = ?

A)
1/2√3

B)
- 1/2√3

C)
1

D)
2√3


Correct Answer :

1/2√3


Explanation :

√(4/3) - √(3/4)
= 2/√3 - √3/2
= (4 - 3)/2√3
= 1/2√3

If √2n = 64, then the value of n is ?

A)
2

B)
4

C)
6

D)
12


Correct Answer :

12


Explanation :

√2n = 64
⇒ 2n/2 = 26
⇒ n/2 = 6
⇒ n = 12

(√5 - √3)/ (√5 + √3) is equal to ?

A)
4 + √15

B)
4 - √15

C)
1/2

D)
1


Correct Answer :

4 - √15


Explanation :

(√5 - √3)/ (√5 + √3)
= (√5 - √3) / (√5 + √3)
= (√5 - √3)2 / (5 - 3)
= (5 + 3 - 2√5 x 3) / 2
= 2 (4 - √15) / 2
= (4 - √15)

3√(0.027/0.125) = ?

A)
0.6

B)
0.3

C)
0.5

D)
0.2


Correct Answer :

0.6


Explanation :

3√(27*1000/125*1000) => 3√(27/125) => 3√27 / 3√125
=> 3√(33) / 3√(53) =>3/4
=> 0.6

The largest three digit number which is a perfect cube is?

A)
986

B)
729

C)
981

D)
864


Correct Answer :

729


Explanation :

93 = 729 and 103 = 1000
So the required number = 729

3√(√ 729) = ?

A)
9

B)
3

C)
8

D)
6


Correct Answer :

3


Explanation :

3√(√ 729) = 3√(√ (272))= 3√27
=> 3√(33) = 3

What is the smallest number by which 1400 be divided to make it a perfect cube?

A)
130

B)
145

C)
160

D)
175


Correct Answer :

175


Explanation :

1400 = 23 * 52 * 7
To make it a perfect cube, it must be divided by
52 *7 = 175

Find the least number by which 175760 be multiplied to make it a perfect cube?

A)
100

B)
160

C)
80

D)
27


Correct Answer :

100


Explanation :

175760 = 24 *5 *133
To make it a perfect cube it must be multiplied by
22 * 52 = 100.

The cube root of 5.832 is ?

A)
0.18

B)
0.28

C)
2.8

D)
1.8


Correct Answer :

1.8


Explanation :

3√5.832 = 3√(5832/1000) =3√5832 / 3√1000 = 18/10 =1.8

The difference of squares of two consecutive odd numbers is always ?

A)
divisible by 8

B)
divisible by 2

C)
divisible by 16

D)
divisible by 18


Correct Answer :

divisible by 8


Explanation :

Let two odd numbers be (2x + 1) and (2x + 3)
Difference between the squares= (2x + 3)2 - (2x + 1)2
= (4x2 + 12x + 9) - (4x2 + 4x + 1)
= 8x+8
= 8(x+1) which is always divisible by 8

Find the value of the following √156.25 + √0.0081 - √0.0361 ?

A)
13.4

B)
15.4

C)
12.4

D)
17.4


Correct Answer :

12.4


Explanation :

√156.25 + √0.0081 - √0.0361
=12.5+0.09-0.19
=12.4

Find the value of √ (0.25 * 2.25) ?

A)
0.075

B)
0.705

C)
0.75

D)
7.500


Correct Answer :

0.75


Explanation :

√ (0.25 * 2.25)
=0.5*1.5
=0.75

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