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Question

You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly guess the cube root of 4913.

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Solution

We already know how to find the cube root of any cube number.
Step 1: Take the given cube number, 1331 and start making groups of three digits starting from the right most digit of the number.
1331––Second GroupFirst group

Step 2: First group i.e., 331 will give us unit's digit of the required cube root.
The number 331 ends with 1. We know that 1 comes at the unit’s place of a number only when it’s cube root ends in 1.
So, we get 1 at the unit’s place of the cube root.

Step 3: Now take another group, i.e., 1.
1 is a cube number so we can take cube root of 1 as the ten’s place of the required cube root.
So, we get 31331=11.

Now Moving on to the second part, We've to find the cube root of the 4913. We will repeat the same steps for this.

Step 1: Take the given cube number, 4913 and start making groups of three digits starting from the right most digit of the number.
4913––Second GroupFirst group

Step 2: First group i.e., 913 will give us unit's digit of the required cube root.
The number 913 ends with 3. We know that 3 comes at the unit’s place of a number only when it’s cube root ends in 7.
So, we get 7 at the unit’s place of the cube root.

Step 3: Now take another group, i.e., 4.
We now that 13=1 and 23=8 and 1<4<8. We take the one’s place of the smaller number as the ten’s place of the required cube root, here it is 1.
So, we get 34913=17.

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