Cubes and Cube Roots – Maharashtra Board Class 8 Solutions for Mathematics
MathematicsGeneral ScienceMaharashtra Board Solutions
Exercise – 45
Solution 1:
Exercise – 46
Solution 1:
i. 63 = 6 × 6 × 6 = 216
ii. (-5)3 = (-5) × (-5) × (-5) = -125
iii. (-10)3 = (-10) × (-10) × (-10) = -1000
iv. 143 = 14 × 14 × 14 = 2744
v. (-12)3 = (-12) × (-12) × (-12) = -1728
Exercise – 47
Solution 1:
Solution 2:
i. The cube root of -512 is -8.
ii. The cube root of 1 is 1.
iii. The cube root of 729 is 9.
iv. The cube root of -729 is -9.
Exercise – 48
Solution 1:
Solution 2(1):
Solution 2(2):
Solution 2(3):
Solution 2(4):
Solution 3(1):
4096 = 4 × 1024
= 4 × 4 × 256
= 4 × 4 × 4 × 64
= 4 × 4 × 4 × 4 × 16
= 4 × 4 × 4 × 4 × 4 × 4
∴ 4096 = 43 × 43 = (4 × 4)3 = 163
Thus, the number 4096 is the cube of the number 16.
Solution 3(2):
4913 = 17 × 17 × 17
∴ 4913 = 173
Thus, the number 4913 is the cube of the number 17.
Solution 3(3):
5832 = 4 × 1458
= 4 × 2 × 729
= 2 × 2 × 2 × 9 × 81
= 2 × 2 × 2 × 9 × 9 × 9
∴ 5832 = 23 × 93 = (2 × 9)3 = 183
Thus, the number 5832 is the cube of the number 18.
Solution 3(4):
Let us first find the cube root of 2197.
2197 = 13 × 13 × 13
∴ 2197 = 133
∴ -2197 = (-13)3
Thus, the number (-2197) is the cube of the number (-13).