Find the cube root of each of the following numbers:(i) 8×125 (ii)

1.	Find the cube root of each of the following numbers:(i) 8×125 (ii) -1728×216
Answer» (i) 8×125 We know that for any two integers a and b, ∛(a×b) = ∛a × ∛b By using the property, ∛ (8×125) = ∛8 × ∛125 = ∛(2×2×2) × ∛(5×5×5) = 2×5 = 10 (ii) -1728×216 We know that for any two integers a and b, ∛(a×b) = ∛a × ∛b By using the property, ∛(-1728×216) = ∛-1728 × ∛216 We shall use the unit digit method, Let the number 1728, where Unit digit = 8 The unit digit in the cube root of 1728 will be 2 After striking out the units, tens and hundreds digits of the given number, we are left with the 1. We know 1 is the largest number whose cube is less than or equal to 1. So, the tens digit of the cube root of 1728 = 1 ∛1728 = 12 Now, let’s find the prime factors for, 216 = 2×2×2×3×3×3 By grouping the factors in triples of equal factor, we get, 216 = (2×2×2) × (3×3×3) ∛216 = 2×3 = 6 From above we take as, ∛(-1728×216) = ∛-1728 × ∛216 = -12 × 6 = -72

Find the cube root of each of the following numbers:(i) 8×125 (ii) -1728×216

Answer»

(i) 8×125

We know that for any two integers a and b, ∛(a×b) = ∛a × ∛b

By using the property,

∛ (8×125) = ∛8 × ∛125

= ∛(2×2×2) × ∛(5×5×5)

= 2×5

= 10

(ii) -1728×216

We know that for any two integers a and b, ∛(a×b) = ∛a × ∛b

By using the property,

∛(-1728×216) = ∛-1728 × ∛216

We shall use the unit digit method,

Let the number 1728, where Unit digit = 8

The unit digit in the cube root of 1728 will be 2

After striking out the units, tens and hundreds digits of the given number, we are left with the 1.

We know 1 is the largest number whose cube is less than or equal to 1.

So, the tens digit of the cube root of 1728 = 1

∛1728 = 12

Now, let’s find the prime factors for,

216 = 2×2×2×3×3×3

By grouping the factors in triples of equal factor, we get,

216 = (2×2×2) × (3×3×3)

∛216 = 2×3

= 6

From above we take as,

∛(-1728×216) = ∛-1728 × ∛216

= -12 × 6

= -72