Aptitude :Square Root and Cube Root

1. The cube root of .000216 is:

A.      0.6

B.      0.06

C.      77

D.      87

Answer: Option B

Explanation:

(.000216)1/3	=		216		1/3
			106

=		6 x 6 x 6		1/3
		102 x 102 x 102

=	6
	102

=	6
	100

   = 0.06

2. What should come in place of both x in the equationx=162.128x

A.     12

B.     14 

C.     144

D.     196

Answer: Option A

Explanation:

Let	x	=	162
	128		x

Then x² = 128 x 162

   = 64 x 2 x 18 x 9

   = 8² x 6² x 3²

   = 8 x 6 x 3

   = 144.

 x = 144 = 12.

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

A.     213444 
B.     214344
C.     214434
D.     231444

Answer: Option A

Explanation:

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


4. 

1.5625 = ?

A. 1.05
B. 1.25
C. 1.45
D. 1.55

Answer: Option B

Explanation:

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

1.5625 = 1.25. 5.  If 35 + 125 = 17.88, then what will be the value of 80 + 65 ?

A. 13.41
B. 20.46
C. 21.66
D. 22.35




Answer: Option D

Explanation:

35 + 125 = 17.88

 35 + 25 x 5 = 17.88

 35 + 55 = 17.88

 85 = 17.88

 5 = 2.235

 80 + 65 = 16 x 5 + 65

   = 45 + 65

   = 105 = (10 x 2.235) = 22.35

6.  If a = 0.1039, then the value of 4a² - 4a + 1 + 3a is:

A. 0.1039
B. 0.2078
C. 1.1039
D. 2.1039

Answer: Option C

Explanation:

4a² - 4a + 1 + 3a = (1)² + (2a)² - 2 x 1 x 2a + 3a
   = (1 - 2a)² + 3a
   = (1 - 2a) + 3a
   = (1 + a)
   = (1 + 0.1039)
   = 1.1039

7. If x =3 + 1and y =3 - 1, then the value of (x² + y²) is:3 - 13 + 1

A. 10

B. 13

C. 14

D. 15 

Answer: Option C

Explanation:

x =	(3 + 1)	x	(3 + 1)	=	(3 + 1)2	=	3 + 1 + 23	= 2 + 3.
	(3 - 1)		(3 + 1)		(3 - 1)		2

y =	(3 - 1)	x	(3 - 1)	=	(3 - 1)2	=	3 + 1 - 23	= 2 - 3.
	(3 + 1)		(3 - 1)		(3 - 1)		2

 x² + y² = (2 + 3)² + (2 - 3)²

   = 2(4 + 3)

   = 14

8.  A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

A. 57
B. 67
C. 77
D. 87

Answer: Option C

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

 Number of members = 5929 = 77.



9. The square  root of (7 + 35) (7 - 35) is


A. 5
B. 2
C. 4
D. 35

Answer: Option B Explanation: (7 + 35)(7 - 35) = (7)2 - (35)2  = 49 - 45  = 4  = 2.

10.  If   5 = 2.236, then the value of

5	-	10	+ 125
2		5			is equal to:

                                                            

                                                            

A. 5.59
B. 7.826
C. 8.944
D. 10.062

Answer: Option B

Explanation:

5	-	10	+ 125	=	(5)2 - 20 + 25 x 55
2		5			25

=	5 - 20 + 50
	25

=	35	x	5
	25		5

=	355
	10

=	7 x 2.236
	2

= 7 x 1.118

= 7.826