squre and root

1. Square and Square Root
1. What is the square root of 0.09?
(1) 0.3 (2) 0.03
(3) 0.003 (4) 3.0
2. The value of
0.441
0.625
is equal to :
(1) 0.048 (2) 0.84
(3) 0.48 (4) 0.084
3.
0.00001225
0.00005329
is equal to :
(1)
25
77
(2)
35
72
(3)
35
77
(4)
25
73
4. The value of
19.36 0.1936 0.001936 0.00001936+ + + is :
(1) 4.8484 (2) 4.8694
(3) 4.8884 (4) 4.8234
5. The fourth root of 24010000 is
(1) 7 (2) 49
(3) 490 (4) 70
6. The square root of 33 4 35- is :
(1) ( )2 7 5± + (2) ( )7 2 5± +
(3) ( )7 2 5± - (4) ( )2 7 5± -
7. The least integer which should be added to 1000 so as to
make it a perfect square is
(1) 10 (2) 18
(3) 24 (4) 89
8. The greatest 4 digit number which is a perfect square, is
(1) 9999 (2) 9909
(3) 9801 (4) 9081
9. The smallest number added to 680621 to make the sum a
perfect square is :
(1) 4 (2) 5
(3) 6 (4) 8
10. The smallest number which should be added to the number
8958 so that the result is a perfect square is
( 1) 69 (2) 67
(3) 77 (4) 79
11. The number, whose square is equal to the differene of the
squares of 75.15 and 60.12, is
( 1) 46.09 (2) 48.09
(3) 45.09 (4) 47.09
12. Three fifth ofthe square of a certain number is 126.15.What
is the number?
( 1) 210.25 (2) 75.69
(3) 14.5 (4) 145
13. The square root of a positive number less than 100 lies
between
( 1) 0 and 1000 (2) 0 and 10
(3) –10 and 10 (4) –100 and 100
14. The sum of the squares of two numbers is 386. If one of the
number is 5, the other will be :
(1) 18 (2) 19
(3) 15 (4) 20
15. The sum of the squares of two positive integers is 100 and
the difference oftheir squares is 28. The sum of the number
is :
( 1) 12 (2) 13
(3) 14 (4) 15
16. If the sum and difference of two numbers are 20 and 8
respectively, then the difference of their square is :
( 1) 12 (2) 28
(3) 80 (4) 160
17. The number, whose square is equal to the difference of the
squares of the numbers 68 and 32, is
( 1) 36 (2) 48
(3) 60 (4) 64
HINTS & SOLUTIONS
.ANSWER KEY.
1. (1) 2. (2) 3. (2) 4. (3) 5. (4) 6. (4)
7. (3) 8. (3) 9. (1) 10. (2) 11. (3) 12. (3)
13. (3) 14. (2) 15. (3) 16. (4) 17. (3)
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2. 2
CAREER POWER
CAREER POWER, G-7, Roots Tower, Laxmi Nagar, District Centre, Delhi-92, www.careerpower.in
Chapterwise SSC Quantitative Aptitude
1. (1) 0.09 = 0.3 0.3´ = 0.3
2. (2) Expression =
0.441
0.625
0.441 441 21
0.84
0.625 625 25
= = = =
3. (2)
0.00001225
0.00005329
8
8
1225
1225 3510
5329 5329 73
10
= = =
4. (3) 19.36 0.1936 0.001936 0.00001936+ + +
= 4.4 + 0.44 + 0.044 + 0.0044 = 4.8884
5. (4) 24010000 = 4900
Again, 4900 = 70
4 24010000 = 70
6. (4) 33 – 4 35 = 33 – 2 × 2 5 7´
= 33 – 2 × 2 7 5´
= 28 5 2 2 7 5+ - ´ ´
= ( ) ( )
2 2
2 7 5 2 2 7 5+ - ´ ´
= ( )
2
2 7 5-
33 4 35- = ( )
2
2 7 5- = ( )2 7 5± -
7. (3) (31)2 < 1000 < 322
32 × 32 = 1024
Required number = 1024 – 1000 = 24
8. (3) 99 × 99 = 9801
9. (1) 8 68 06 21
824
8 64
162 406
2 324
1644 8221
6576
1645
(824)2 < 680621 < 8252
Required number = [(825)2 – 680621] = 4
10. (2) 9 89 58
94
9 81
184 858
4 736
188 8221
6578
122
Now, 95 × 95 = 9025
Required number = 9025 – 8958 = 67
11. (3) Let the number be x. Then,
x2 = (75.15)2 – (60.12)2
= (75.15 + 60.12) (175.15 + 60.12)
= 135.27 × 15.03 = 2033.1081
2033.1081xÞ = = 45.09
12. (3) Let the number be x
According to the question
3
5
of x2 = 126.15
2 126.15 5
3
x
´
Þ = = 210.25
210.25 14.5x = =
13. (3) Since the numbers between –10 and 10 will be single
digit and the numbers below 100 will be either one
digit or two digit. We know that the square root ofone
or two digit number is always single digit number.
Therefore, required answer is option (3).
14. (2) Let the required number be x. Then
x2 + 52 = 386
Þ x2 = 386 – 25
Þ x = 361
Þ x = 361 = 19
15. (3) Let the numbers be x and y.
Then,
x2 + y2 = 100 ...(i)
x2 – y2 = 28 ...(ii)
On adding,
2x2 = 128
Þ x2 = 64 Þ x = 8
From equation (i),
64 + y2 = 100
Þ y2 = 36 Þ y = 6
Required sum = 8 + 6 = 14
16. (4) Let x + y = 20 and x – y = 8
(x + y) (x – y) = 20 × 8
Þ x2 – y2 = 160
17. (3) According to the question,
= 682 – 322 = (68 + 32) (68 – 32)
= 100 × 36 = 3600 = (60)2
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