Finding the Cube Roots of the Cubic Numbers Through the Estimation Method

Cube Root of a Cube Number:

1) Find the cube root of 857375 through estimation.

Step 1: Take any cube number say 857375 and start making groups of three digits starting from the rightmost digit of the number.

We can estimate the cube root of a given cube number through a step by step process.
We get 375 and 857 as two groups of three digits each.

Step 2: First group, i.e., 375 will give you the one’s (or unit’s) digit of the required cube root.

The number 375 ends with 5. We know that 5 comes at the unit’s place of a number only when it’s cube root ends in 5.

So, we get 5 at the unit’s place of the cube root.

Step 3: Now take another group, i.e., 857.
We know that 9³ = 729 and 10³ = 1000. Also, 729 < 857 < 1000.

We take the one’s place, of the smaller number 729 as the ten’s place of the required cube root.

So, we get `root(3)(857375) = 95`.