#### notes

If you know that the given number is a cube number then following method can be used.**Step 1:** Take any cube number say 857375 and start making groups of three digits starting from the right most 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 \[\sqrt[3]{857375}\] = 95.