Question

Find the cube root of the following by looking at the last digit and using estimation:

(i) 91125; (ii) 166375; (iii) 704969.

Answer 1

(i) Let n³ = 91125

Here, the units digits is 5; therefore, the units digit of n must be 5.

Let us split the number 91125 as 91 and 125

Now, 4³ < 91 < 5³ = 125

∴ 40³ = 64000 < 91000 < 50³ = 125000

Since the units digit of n is 5, the only possible number is 45.

It can be verified that

(ii) Let n³ = 166375

Here, the units digits is 5; therefore, the units digit of n must be 5.

Let us split the number 166375 as 166 and 375.

Now, 5³ = 125 < 166 < 6³ = 216

∴ 50³ = 125000 < 166000 < 60³ = 216000

Since the units digit of n is 5, the only possible number is 55.

It can be verified that

(iii) Let n³ = 704969.

Here, the units digits is 9; therefore, the units digit of n must be 9.

Let us split the number 704969 as 704 and 969.

Now, 8³ = 512 < 704 < 9³ = 729

∴ 80³ = 512000 < 704000 < 90³ = 729000

Since the units digit of n is 9, the only possible number is 89.

It can be verified that