# You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768

**Solution:**

By grouping the digits of the number into triplets starting from one's digit

(i) 1331

Step 1: 1 = Group 2 and 33__1__ = Group 1

Step 2: From group 1, one’s digit of the cube root can be identified.

33__1__= One’s digit is 1

Hence cube root one’s digit is 1.

Step 3: From group 2, which is 1 only.

Hence cube root’s ten’s digit is 1.

So, we get ∛1331 = 11.

(ii) 4913

Step 1: 4 = Group 2 and 91__3__ = Group 1

Step 2: From group 1, which is 913.

91__3__ = One’s digit is 3

We know that 3 comes at the one’s place of a number only when its cube root ends in 7. So, we get 7 at the one’s place of the cube root. (Refer to table 7.2 INFERENCE)

Step 3: From Group 2, which is 4.

1^{3} < 4 < 2^{3}

Taking lower limit. Therefore, the ten’s digit of cube root is 1.

So, we get ∛1331 = 17

(iii) Similarly, we get ∛12167 = 23

(iv) Similarly, we get ∛32768 = 32

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 7

**Video Solution:**

## You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768

NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 Question 3

**Summary:**

You are told that 1,331 is a perfect cube. The cube root of 1,331 is 11. Similarly, the cube roots of 4913, 12167, 32768 are 17, 23, and 32

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