How to guess cube root without factorisation

Solution:

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

(i) 1331

Step 1: 1 = Group 2 and 331 = Group 1

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

331= 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 913 = Group 1

Step 2: From group 1, which is 913.

913 = 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.

13 < 4 < 23

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:

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

☛ Related Questions:

 By grouping the digits, we get 1 and 331

We know that, since, the unit digit of cube is 1, the unit digit of cube root is 1.

∴ We get 1 as unit digit of the cube root of 1331.

The cube of 1 matches with the number of second group.

∴ The ten's digit of our cube root is taken as the unit place of smallest number.

We know that, the unit’s digit of the cube of a number having digit as unit’s place 1 is 1.

\therefore \sqrt[3]{1331}=11

 By grouping the digits, we get 4 and 913

We know that, since, the unit digit of cube is 3, the unit digit of cube root is 7.

∴ we get 7 as unit digit of the cube root of 4913.

We know 1^{3}=1 \text { and } 2^{3}=8 , 1 > 4 > 8.

Thus, 1 is taken as ten digit of cube root.

\therefore \sqrt[3]{4913}=17

 By grouping the digits, we get 12 and 167.

We know that, since, the unit digit of cube is 7, the unit digit of cube root is 3.

∴ 3 is the unit digit of the cube root of 12167

We know 2^{3}=8 \text { and } 3^{3}=27, 8 > 12 > 27.

Thus, 2 is taken as ten digit of cube root.

\therefore \sqrt[3]{12167}=23

 By grouping the digits, we get 32 and 768.

We know that, since, the unit digit of cube is 8, the unit digit of cube root is 2.

∴ 2 is the unit digit of the cube root of 32768.

We know 3^{3}=27 \text { and } 4^{3}=64, 27 > 32 > 64.

Thus, 3 is taken as ten digit of cube root.

\therefore \sqrt[3]{32768}=32