Aptitude :: Square Root
and Cube Root
Important Formulas
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
x x x y xy
2. = = x = .
y y y y y
Square Root and Cube Root > General Questions
1. The cube root of .000216 is:
A..6
C. 77
Answer & Explanation
B. .06
D.87
Answer: Option B
Explanation:
216 1/3
106
6x6x6
1/3
=
102 x 102 x 102
6
= 2
10
6
=
100
(.000216)1/3=
= 0.06
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2.
x 162
What should come in place of both x in the equation =
.
128 x
A.12
B. 14
C. 144
D.196
Answer & Explanation
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
=8x6x3
= 144.
x = 144 = 12.
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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
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4. 1.5625 = ?
A.1.05
C. 1.45
Answer & Explanation
Answer: Option B
Explanation:
1|1.5625( 1.25
|1
|------22| 56
| 44
|------245| 1225
| 1225
|------|
X
|-------
1.5625 = 1.25.
B. 1.25
D.1.55
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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
= 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 & 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
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7.
3+1
3-1
and y =
, then the value of (x2 + y2) is:
3-1
3+1
A.10
B. 13
C. 14
D.15
Answer & Explanation
If x =
Answer: Option C
Explanation:
(3 + 1) (3 + 1) (3 + 1)2 3 + 1 - 23
x
=
=
= 2 + 3.
(3 - 1) (3 + 1) (3 - 1)
2
(3 - 1) (3 - 1) (3 - 1)2 3 + 1 - 23
y=
x
=
=
= 2 - 3.
(3 + 1) (3 - 1) (3 - 1)
2
x=
x2 + y2 = (2 + 3)2 + (2 - 3)2
= 2(4 + 3)
= 14
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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.
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9. The square root of (7 + 35) (7 - 35) is
A.5
B. 2
C. 4
Answer & Explanation
D.35
Answer: Option B
Explanation:
(7 + 35)(7 - 35)=(7)2 - (35)2 = 49 - 45 = 4 = 2.
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10.
5 10
If 5 = 2.236, then the value of - + 125 is equal to:
2 5
A.5.59
B. 7.826
C. 8.944
D.10.062
Answer & Explanation
Answer: Option B
Explanation:
5 10
(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
= 7 x 1.118
= 7.826
11.
625 14 11
x x
is equal to:
11 25 196
A.5
C. 8
Answer & Explanation
Answer: Option A
Explanation:
25 14 11
Given Expression = x x = 5.
11 5 14
B. 6
D.11
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12. 0.0169 x ? = 1.3
A.10
C. 1000
Answer & Explanation
B. 100
D.None of these
Answer: Option B
Explanation:
Let 0.0169 x x = 1.3.
Then, 0.0169x = (1.3)2 = 1.69
1.69
= 100
0.0169
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x=
13.
1
3 - 2simplifies to:
3
3
A.
4
4
C.
3
Answer & Explanation
B.
4
3
D.None of these
Answer: Option C
Explanation:
1
1
1
3 - 2= (3)2 +
2- 2 x 3 x
3
3
3
1
=3+ -2
3
1
=1+
3
4
=
3
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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.
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15. The square root of 64009 is:
A.253
C. 363
Answer & Explanation
Answer: Option A
Explanation:
2|64009( 253
|4
|---------45|240
|225
|---------503| 1509
| 1509
|---------|
X
|----------
64009 = 253.
B. 347
D.803