Question

Find the cube root of 103823 by prime factorisation method.

Answer 1

Here unit in the digits place is 3. If n³ = 103823. Then, the unit in the digits place of n must be 7 as $7^3$ contains 3 in its unit place.

Let us split this as 103 and 823.

We observe that, 4³ = 64 < 103 < 125 = 5³.

Hence 40³ = 64000 < 103823 < 125000 = 50³.
Hence n must lie between 40 and 50.
Since the unit in the digits place is 7.
Therefore n must be 47.
Hence, 47³ = 103823.