Class 8: Cube Roots – Exercise 7 C
1. Find the cubes of:
i.
16
163 = 16 x 16 x 16 = 4096
ii.
iv.
0.73 = 0.7 x 0.7 x 0.7 = 0.343
30
303 = 30 x 30 x 30 =
v.
27000
iii.
0.7
0.06
0.063 = 0.06 x 0.06 x 0.06 =
1.2
0.000216
1.23 = 1.2 x 1.2 x 1.2 =
vi.
1.728
vii.
viii.
2 3
( ) =
5
8
125
1 3
( ) =
9
1
729
3 3
512
5
125
(1 ) =
2. Test whether the given number is a perfect cube or not:
i.
729 = 7 x 7 x 7 (hence a perfect cube)
ii.
3380 = 4 x 5 x 13 x 13 (hence not a perfect cube)
iii.
10584 = 8 x 3 x 3 x 3 x 3 x 7 x 7 (hence not a perfect cube)
iv.
13824 = (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2) x (3 x 3 x 3) (hence a perfect
cube)
3. Find the smallest number by which 11979 must be multiplied so that the product is a
perfect cube.
11979 = 3 x 3 x 11 x 11 x 11
Therefore multiply the number by 3 for it to be a perfect cube.
1
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4. Find the smallest number by which 8788 must be divided so that the quotient is a perfect
cube.
8788 = 2 x 2 x 13 x 13 x 13
Hence divide the number by 4 so that the quotient is a perfect square
5. Find the cube root of:
i.
1728 = 23 x 23 x 33 Therefore the cube root of 1728 is 12
ii.
5832 = 23 x 93 Therefore the cube root of 5832 is 18
iii.
10648 = 23 x 113 Therefore the cube root of 10648 is 22
iv.
35937 = 33 x 113 Therefore the cube root of 35937 is 33
216
v.
2197
4
vi.
6×6×6
=
508
1331
13×13×13
5832
=
Therefore the cube root of
=
1331
42875
=
vii.
42.875 =
viii.
0.000110592 =
1000
2×2×2×9×9×9
11×11×11
10×10×10
110592
=
2197
is
6
13
Therefore the cube root of 4
5×5×5×7×7×7
1000000000
216
508
1331
=
18
11
Therefore the cube root of 42.875 is 3.5
4×4×4×4×4×4×3×3×3
1000×1000×1000
Therefore the cube root of
0.000110592 is 0.048
6. Evaluate:
i.
3
3
√1352 × √1625
3
3
= √2 × 2 × 2 × 13 × 13 × √5 × 5 × 5 × 13
= 2 × 5 × 13 = 130
ii.
iii.
iv.
3
√
51.2
0.4096
3
= √
512000
4096
3
= √
2×2×2×2×2×2×2×2×2×10×10×10
2×2×2×2×2×2×2×2×2×2×2×2
=5
3
√√0.000064 = 3√0.008 = 0.2
3
√√0.004096 + 3√0.729
3
= √0.064 + 0.9 = 0.4 + 0.9 = 1.3
2
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