## Chapter 7 Cubes and Cube Roots Exercise 7.2

**Question 1: Find the cube root of each of the following numbers by prime factorisation method.**

(i) 64

(ii) 512

(iii) 10648

(iv) 27000

(v) 15625

(vi) 13824

(vii) 110592

(viii) 46656

(ix) 175616

(x) 91125

Answer:

(i) 64

(ii) 512

(iii) 10648

(iv) 27000

(v) 15625

(vi) 13824

(vii) 110592

(viii) 46656

(ix) 175616

(x) 91125

Answer:

(i)

(ii)

Therefore, the cube root of 512 is 8.

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

**Question 2: State true or false.**

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeros.

(iii) If square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8.

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

Answer:

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeros.

(iii) If square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8.

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

Answer:

(i) False

(ii) True

(iii) False

(iv) False

(v) False

(vi) False

(vii) True

**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.**

Answer:

Answer:

• 1331

Form groups of three starting from the rightmost digit of 1331.

1 3 3 1

Take 331. If the number ends with 1, its unit digit of cube root will be 1.

Take 1 (other group).

= 1³ = 1

= 2³ = 8

= 1³ = 1 < 2³

The one’s place of 1 is 1 itself. Take 1 as ten’s place of the cube root of 1331.

Therefore, ∛1331 = 11

• 4913

Form groups of three starting from the rightmost digit of 1331.

4 9 1 3

Take 913. If the number ends with 3, its unit digit of cube root will be 7.

Take 4 (other group).

= 1³ = 1

= 2³ = 8

= 1³ < 4 < 2³

The one’s place of 1 is 1 itself. Take 1 as ten’s place of the cube root of 4913.

Therefore, ∛4913 = 17

• 12167

Form groups of three starting from the rightmost digit of 1331.

1 2 1 6 7

Take 167. If the number ends with 7, its unit digit of cube root will be 3.

Take 12 (other group).

= 2³ = 8

= 3³ = 27

= 2³ < 12 < 3³

The one’s place of 2 is 2 itself. Take 2 as ten’s place of the cube root of 12167.

Therefore, ∛12167 = 22.

• 32768

Form groups of three starting from the rightmost digit of 32768.

3 2 7 6 8

Take 768. If the number ends with 8, its unit digit of cube root will be 2.

Take 32 (other group).

= 3³ = 27

= 4³ = 64

= 3³ < 32 < 4³

The one’s place of 3 is 3 itself. Take 3 as ten’s place of the cube root of 32768.

Therefore, ∛32768 = 32.

## No comments:

## Post a Comment