Question

Find the nearest integer to the cube root of each of the following:

(i) 331776; (ii) 46656; (iii) 373248.

Answer 1

(i) 331776

We observe that 6³ = 216 < 331 < 7³ = 343

∴ 60³ = 216000 < 331000 < 70³ = 343000

Now, 69³ = 328509

Therefore, must lie between 69 and 70.

Moreover, 331776 is nearer to 328509 than to 343000.

Hence, the closest integer tois 69.

(ii) 46656

We observe that 3³ = 27 < 46 < 4³ = 64

∴ 30³ = 27000 < 46000 < 40³ = 64000

Now, 31³ = 29791, 32³ = 32768, 35³ = 42875, 36³ = 46656

∴

(iii) 373248

We observe that 7³ = 343 < 373 < 8³ = 512

∴ 70³ = 343000 < 373000 < 80³ = 512000

Now, 71³ = 357911, 72³ = 373248

∴