Class 8: Square Roots - Exercise 7B
1. Find the square root of:
i.
5.4289
2
43
5
4
1
1
.
42
29
13
13
0
463
ii.
42
2.33
89
89
176.252176
1
1
1
23
76
25
.
76
69
7
5
2
1
262
2647
25
24
01
85
15
15
26546
iii.
89
21
21
29
92
92
0
76
13.276
76
76
18.1476
4
82
846
18
16
2
1
.
14
14
64
50
50
0
76
4.26
76
76
1
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iv.
0.018769
1
0
.
23
01
1
0
87
87
69
18
18
262
v.
0.137
69
69
0
67.0761
8
67
64
3
1
1
1
161
1629
vi.
69
.
07
07
61
46
46
0
61
8.19
61
61
0.00038809
1
29
0
.
00
03
01
2
2
387
88
88
61
27
27
0
09
0.0197
09
09
2. Find the value of each of the following up to 3 decimal places :
2
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i.
√2
1
24
2
1
1
.
00
96
4
2
1
1
281
2824
ii.
00
1.414
00
81
19
12
6
00
96
14
√7
2
46
7
4
3
2
.
00
00
76
24
20
3
2
524
5285
iii.
00
00
00
00
96
14
64
49
00
25
75
00
00
00
61
39
23
15
00
16
84
2.645
√27
5
101
1029
10386
27
25
2
1
.
00
00
01
99
92
6
6
5.196
3
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iv.
√2.469
1
25
2
1
1
1
.
46
90
00
90
49
41
31
9
00
41
59
72
00
00
72
70
1
1
00
49
51
01
49
00
41
59
46
25
21
21
307
3141
v.
√25.72
5
25
25
.
1007
10141
vi.
1.571
5.071
√0.4
6
123
0
.
40
36
4
3
1262
00
00
00
69
31
25
5
00
24
72
0.632
4
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3. Find the value of each of the following correct to 2 places of decimal:
i.
√11 = 3.32
3
63
11
9
2
1
.
00
89
11
6
4
3
661
6626
ii.
25
2
1
1
1
.
40
40
25
15
12
2
2
304
3089
00
00
61
39
97
41
00
56
44
00
00
00
16
84
78
5
00
01
99
90
00
90
69
21
18
2
00
69
31
3.316
1.549
√0.019 = 0.14
1
0
.
01
01
23
267
iv.
00
√2.4 = 1.55
1
iii.
00
0.137
√0.121 = 0.35
5
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3
0
64
.
12
9
3
2
687
10
00
10
56
54
48
5
00
09
91
0.347
4. Find the square root of:
1089
i.
4624
1089
33 × 33
33
√
= √
=
4624
68 × 68
68
25
ii.
√25
√3
iv.
729
544
18769
137
2
= √
=
=5
729
729
27
27
3
iii.
544
942
2209
942
7569
87
40
= √
=
=1
2209
2209
47
47
42
√42
583
1369
583
58081
241
19
= √
=
=6
1369
1369
37
37
6
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5. Find the value of:
√243
√867
i.
=√
ii.
=√
243
81
9×9
9
= √
= √
=
867
289
17 × 17
17
√4352
√12393
4352
8 × 2 × 2 × 2 × 2 × 2 × 17
2×2 ×2× 2×2×2 ×2× 2
16
= √
= √
=
12393
3 × 3 × 3 × 3 × 3 × 3 × 17
3×3×3×3×3×3
27
3
6. Find the value of √ correct to 2 places of decimal.
8
3
6
√6 2.44
√ = √ =
=
= 0.61
8
16
4
4
7. Find the value of √15625 and hence evaluate √156.25 + √1.5625
√15625 = √25 × 625 = 5 × 25 = 125
√156 · 25 =
√1.5625 =
√15625
√100
√15625
√10000
=
=
125
= 12.5
10
125
= 1.25
100
Therefore √156.25 + √1.5625 = 13.75
7
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8. Find the value of √103 · 0225 and hence find the square root of:
√103.0225 =
i.
√10000
=
1015
= 10.15
100
=
1015
= 101.5
10
10302.25
√10302.25 =
ii.
√1030225
√1030225
√100
0.01030225
√0.01030225 =
√1030225
√100000000
=
1015
= 0.1015
10000
9. Evaluate
i.
√99 × √396
= √(100 − 1) × √(400 − 4)
= √(100 − 1) × √(100 − 1) × 4
= (100 − 1) × 2 = 99 × 2 = 198
ii.
√147 × √243
= √7 × 7 × 3 × √3 × 9 × 9
= 7 × 3 × 9 = 189
10. Evaluate
i.
√
=√
0.289
0.00121
0.289
28900
170
5
= √
=
= 15
0.00121
121
11
11
8
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ii.
√
=√
iii.
48.4
0.289
48.4
48400
220
16
= √
=
= 12
0.289
289
17
17
√0.01 + √0.0064
= √0.01 + √0.0064
= √0.01 + 0.08
= √0.09 = 0.03
iv.
√0.01 + √0.81 + √1.21 + √0.0009
= 0.1 + 0.09 + 1.1 + 0.03 = 2.13
v.
√41 − √21 + √19 − √9
= √41 − √21 + √19 − 3
= √41 − √21 + 4
= √41 − 5 = 6
9
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vi.
√10 + √25 + √108 + √154 +
√225
= √10 + √25 + √108 + √154 + 15
= √10 + √25 + √108 + 13
= √10 + √25 + 11
= √10 + 6 = 4
11. Three-fifth of the square of a certain number is 126.15. Find the number.
3 2
𝑥 = 126.15
5
𝑥 2 = 210.25 𝑜𝑟 𝑥 = 14.5
12. A square plot of land has area equal to that of a rectangular plot having length 218.79 meters
and breadth 24.31 meters. Find the perimeter of the square plot.
𝑥 2 = 218.79 × 24.13 𝑜𝑟 𝑥 = 72.93
Therefore Perimeter = 4 × 72.93 = 291.72 meters
10
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