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 |