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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

Solution:

(i) Cube of any odd number is even.

False

Reasoning: Cubes of odd numbers are odd. Cubes of even numbers are even.

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

True

Reasoning: Perfect cube may end with 3 zeros (or) groups of 3 zeros.

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

False

Reasoning:

It is not always necessary that if the square of a number ends with 5, then its cube will end with 25.

For example, the square of 5 is 25, and 25 has its unit digit as 5. The cube of 5 is 125. However, the square of 15 is 225 and also has its unit place digit as 5 but the cube of 15 is 3375 which does not end with 25.

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

False

Reasoning:

The cubes of all the numbers having their unit place digit as 2 will end with 8.

For example: The cube of 12 is 1728 and the cube of 22 is 10648.

(v) The cube of a 2-digit number may be a 3-digit number.

False

Reasoning: Cube of a 1-digit number may have 1-digit to 3-digits. Cube of a 2-digit number may have 4-digits to maximum 6-digits.

(vi) The cube of a 2-digit number may have seven or more digits.

False

Reasoning: Cube of a 1-digit number may have 1-digit to 3-digits. Cube of a 2-digit number may have 4-digits to maximum 6-digits.

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

True

Reasoning: Some examples 1³ = 1 and 2³ = 8

(viii) Cube of any odd number is even.

False

Reasoning: Cubes of odd numbers are odd. Cubes of even numbers are even.

(ix) Cube of any odd number is even.

False

Reasoning: Cubes of odd numbers are odd. Cubes of even numbers are even.

(x) Cube of any odd number is even.

False

Reasoning: Cubes of odd numbers are odd. Cubes of even numbers are even.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 7

Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.2 Question 2

Summary:

The answers to the given statements (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 numberare (i) False, (ii) True, (iii) False, (iv) False, (v) False, (vi) False, (vii) True, (viii) False, (ix) False and (x) False

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