# 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:**

Reasoning: By grouping the digits of the number into 3 and using Table 7.2

(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

**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

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

The cube roots of the given numbers are (i) 11, (ii) 17, (iii) 23, and (iv) 32