Square Root and Cube Root
1.
The cube root of .000216 is:
A.
.6
B.
.06
C.
77
D.
87
Answer & Explanation
Answer: Option B
Explanation:
216 1/3
(.000216)1/3
=
106
1/3
6x6x6
=
2
2
10 x 10 x 10
2
6
=
102
6
=
100
= 0.06
2.
What should come in place of both x in the equation
x
128
=
162
.
x
A.
12
B.
14
C.
144
D.
196
Answer & Explanation
Answer: Option A
Explanation:
x
Let
=
128
162
x
Then x2 = 128 x 162
= 64 x 2 x 18 x 9
= 82 x 62 x 32
=8x6x3
= 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 & Explanation
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 & Explanation
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 & Explanation
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
6.
= 105 = (10 x 2.235) = 22.35
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 & Explanation
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+1
3-1
and y =
3-1
3+1
, then the value of (x2 + y2) is:
A.
10
B.
13
C.
14
D.
15
Answer & Explanation
Answer: Option C
Explanation:
(3 + 1)
x=
(3 - 1)
(3 - 1)
y=
(3 + 1)
x
x
(3 + 1)
(3 + 1)
(3 - 1)
(3 - 1)
=
=
(3 + 1)2
(3 - 1)
(3 - 1)2
(3 - 1)
=
=
3 + 1 + 23
2
3 + 1 - 23
2
= 2 + 3.
= 2 - 3.
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 & Explanation
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 & Explanation
Answer: Option B
Explanation:
(7)2 - (35)2 = 49 - 45 = 4 = 2.
(7 + 35)(7 - 35) =
10.
If 5 = 2.236, then the value of
5
2
-
10
5
+ 125 is equal to:
A.
5.59
B.
7.826
C.
8.944
D.
10.062
Answer & Explanation
Answer: Option B
Explanation:
(5)2 - 20 + 25 x 55
+ 125 =
2
5
25
5 - 20 + 50
=
25
35
5
=
x
25
5
355
=
10
7 x 2.236
=
2
5
10
-
= 7 x 1.118
= 7.826
11.
625
11
14
x
25
11
x
is equal to:
196
A.
5
B.
6
C.
8
D.
11
Answer & Explanation
Answer: Option A
Explanation:
Given Expression =
25
11
x
14
5
x
11
14
= 5.
12. 0.0169 x ? = 1.3
A.
10
B.
100
C.
1000
D.
None of these
Answer & Explanation
Answer: Option B
Explanation:
Let 0.0169 x x = 1.3.
Then, 0.0169x = (1.3)2 = 1.69
x=
13.
1.69
0.0169
= 100
1 2
3-
A.
simplifies to:
3
3
4
B.
4
3
4
C.
D.
3
None of these
Answer & Explanation
Answer: Option C
Explanation:
1 2
3=3+
=1+
=
3
1
3
1
= (3)2 +
1 2
3
1
-2x3x
3
-2
3
4
3
14. How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the
two-digit number is 8 ?
A.
1
B.
2
C.
3
D.
None of these
Answer & Explanation
Answer: Option D
Explanation:
A number ending in 8 can never be a perfect square.
15. The square root of 64009 is:
A.
253
B.
347
C.
363
D.
803
Answer & Explanation
Answer: Option A
Explanation:
2|64009( 253
|4
|---------45|240
|225
|---------503| 1509
| 1509
|---------|
X
|---------64009 = 253.
1. Square Root:
If x2 = y, we say that the square root of y is x and we write y = x.
Thus, 4 = 2, 9 = 3, 196 = 14.
2. Cube Root:
The cube root of a given number x is the number whose cube is x.
We, denote the cube root of x by x.
Thus, 8 = 2 x 2 x 2 = 2, 343 = 7 x 7 x 7 = 7 etc.
Note:
1. xy = x x y
2.
x
y
=
x
y
=
x
y
x
y
y
=
xy
y
.
11. 13937.869 ÷ 199.54 + 15% of 201 = ?. [Bank PO 1994]
150
80
90
100
Answer & Explanation
Answer:
100
Explanation: Given Exp = 13937.869 / 199.54 +15/100*201 = 69.85 + 30.15 = 100
12. One fourth of one third of two fifth of a number is 15. What will be40% of that number?. [Bank PO 1994]
120
270
350
180
Answer & Explanation
Answer:
180
Explanation: (1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180
13. The population of a town has increased from 133575 to 138918. The percent increase in population is. [Clerks
Grade 19]
2.5
3.5
3
4
Answer & Explanation
Answer:
4
Explanation: increase on 133575 = 138918 - 133575 = 5343
increase on 100 = 5343/133575 *10 = 4