Question

Find the cube root of 110592 by estimation form

Answer 1

110 592
The unit digit of 592 is 2.
So, the unit digit of required cube root is 8.
Now, 43<110<53
64<110<125
643<1103<1253
4<1103<5The smallest number is 4.
Therefore, the cube root of 110592 is 48.

Answer 2

First, some observations:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
10^3 = 1000

We observe that if the units digit of a perfect cube is...

• 1 → units digit of cube root is 1
• 2 → units digit of cube root is 8
• 3 → units digit of cube root is 7
• 4 → units digit of cube root is 4
• 5 → units digit of cube root is 5
• 6 → units digit of cube root is 6
• 7 → units digit of cube root is 3
• 8 → units digit of cube root is 2
• 9 → units digit of cube root is 9
• 0 → units digit of cube root is 0

Given number is 110592

As it's a six digit number, cube root must be of two digits.

Consider the last three digits:
592

Here the last digit is 2. This means that if 110592 is a perfect cube, it's cube root must end in 8


Thus, as last digit is 2, the last digit of it's cube root must be 8.

Now, consider the first three digits:
110

110 lies between the two perfect cubes 64 (4^3) and 125 (5^3)

Thus 110592 must lie between 40^3 and 50^3 . And as last digit is 8,
cube root is 48.