Page 63 - ICSE Math 8

MENTAL MATHS

1. Choose the correct option.

(a) Cube of an odd natural number is:
(i) a prime number (ii) an even natural number
(iii) an odd natural number (iv) none of these

(b) Cube root of –729 is:
(i) 9 (ii) –9 (iii) 81 (iv) –3
(c) Cube root of the product of a positive and a negative number is:
(i) a prime number (ii) a positive number
(iii) a negative number (iv) may be positive or negative

(d) The value of 3 −3 3 is:

3
3
(i) –3 (ii) 3 (iii) –3 (iv) 3
2. Write True or False.
(a) 9,261 is a perfect cube.

(b) There is no perfect cube that ends in 4.
(c) No perfect cube can end with exactly two zeros.
3
3
(d) If x divides y, then x divides y .
3
2
2
3
(e) If m and n are integers such that m > n , then m > n .
3
2
(f) If x ends in an even number of zeros, then x ends in an odd number of zeros.
3
2
(g) If x ends in 5, then x ends in 25.
3. Fill in the blanks.
(a) The units digit of the cube of 388 is ____________.
(b) If a number is multiplied by 4, its cube gets multiplied by ____________.
(c) 3 2 744, =¥ _______
2
(d) 3 480 = ___ ¥ 2 ¥ 3 20
3

PRACTICE TIME

1. Find the cubes of the following numbers.
(a) 19 (b) 26 (c) 49 (d) 123
2. Find the smallest number by which 1,458 must be divided to make it a perfect cube.
3. Find the smallest number by which 675 must be multiplied to make it a perfect cube.
4. Find the cube roots of the following.
(a) –4,913 × 512 (b) 729 × 4,096 (c) –1,331 × (–2,744)
27
(d) – (e) 0.000036 (f) –1,75,616.
125
3
5. A cubical box is length 8 cm. How many cubical boxes of column 8 cm can be placed inside it?
3
6. The volume of a cubical box is 24,60,375 cm . Find the length of its side.

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