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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 1^{3} = 1 and 2^{3} = 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

**☛ Related Questions:**

- Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.(i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100
- Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704.
- Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
- Find the cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125

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