**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).