Practice Set 3.3 8th Std Maths Answers Chapter 3 Indices and Cube Root
Question 1
Maharashtra Board Solution
Find the cube root of the following numbers. i. 8000 ii. 729 iii. 343 iv. -512 v. -2744 vi. 32768
Solution & Step-by-Step Answer:
i. 8000 = 2 × 2 × 2 × 10 × 10 × 10 = (2 × 10) × (2 × 10) × (2 × 10) = (2 × 10)³ = 20³ ∴
ii. 729
= (3 × 3) × (3 × 3) × (3 × 3)
= (3 × 3)³
= 9³
∴
iii. 343
= 7 × 7 × 7
= 7³
∴
iv. -512
= 2 × 2 × 2 × 4 × 4 × 4
= (2 × 4) × (2 × 4) × (2 × 4)
= (2 × 4)³
= 8³
∴ – 512 = (- 8) × (- 8) × (- 8)
= (-8)³
∴
v. -2744
= 2 × 2 × 2 × 7 × 7 × 7
= (2 × 7) × (2 × 7) × (2 × 7)
= (2 × 7)³
= 14³
∴ -2744 = (-14) × (-14) × (-14)
= (-14)³
∴
vi. 32768
= 2 × 2 × 2 × 4 × 4 × 4 × 4 × 4 × 4
= (2 × 4 × 4) × (2 × 4 × 4) × (2 × 4 × 4)
= (2 × 4 × 4)³
= 32³
∴
Question 2
Maharashtra Board Solution
Simplify: i. ii. iii. If then = ?
Solution & Step-by-Step Answer:
i.
ii.
iii.
Note:
Here, number of decimal places in cube root = 6
∴ number of decimal places in cube of number = 2
Maharashtra Board Class 8 Maths Chapter 3 Indices and Cube Root Practice Set 3.3 Intext Questions and Activities
Question 1
Maharashtra Board Solution
17 is a positive number. The cube of 17, which is 4913, is also a positive number. Cube of -6 is -216. Take some more positive and negative numbers and obtain their cubes. Find the relation between the sign of a number and the sign of its cube. (Textbook pg. no. 17)
Solution & Step-by-Step Answer:
Consider, 6³ = 6 × 6 × 6 = 216 and (-4)³ = (- 4) × (- 4) × (- 4) = – 64 Thus, cube of a positive number is positive and cube of a negative number is negative. ∴ Sign of a number = sign of its cube.
Question 2
Maharashtra Board Solution
In example 4 and 5 on textbook pg. no. 17, observe the number of decimal places in the number and number of decimal places in the cube of the number. Is there any relation between the two? (Textbook pg. no. 17)
Solution & Step-by-Step Answer:
Yes, there is a relation between the number of decimal places in the number and its cube. (1.2)³ = 1.728, (0.02)³ = 0.000008 No. of decimal places in 1.2 = 1 No. of decimal places in 1.728 = 3 No. of decimal places in 0.02 = 2 No. of decimal places in 0.000008 = 6 Thus, number of decimal places in cube of a number is three times the number of decimal places in that number.