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Cube Roots - Cube Root of a Cube Number

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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.

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