Page 62 - ICSE Math 8

EXERCISE 4.3

1. Find the cube roots of the following.
(a) –343 (b) –0.729 (c) –6,859 (d) –3,73,248 (e) 2.197
2. Prove that:

(a) 3 8 ¥ 3 27 = 3 8 ¥ 27 (b) 3 125 ¥ 3 216 = 3 125 ¥ 216

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(c) 3 -512 ¥ 343 =-512 ¥ 343 (d) 3 -729 ¥ -1 000(, ) = -729 ¥ -1 000,
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3. Evaluate the following.
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(a) 3 81 331× , (b) -125 729 (c) -64 ¥ -343( ) (d) 6 × 8 3
¥
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125 8 0 729. 009.
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(e) 125 p − 3 125p (f) 1 331, + 3 0 027. - 3 0 008. (g) 3 512 × 5 (h) 3 4 096. ÷ 016.
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4. Find the cube roots of the following rational numbers.
729 −3 375, 24 389, 9 261, −21 952,
(a) (b) (c) (d) (e)
2 197, 4 913, 19 683, − 1 000, 6 859,
5. Find the smallest number by which –6,125 should be multiplied to make it a perfect cube.
6. Find the smallest number by which –250 should be divided to make it a perfect cube.
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7. The volume of a cuboidal box is 35.937 m . Find the side of the box.
2 197,
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8. The volume of a cube is cm . Find its side.
729
9. Find the cube of 12 by using its prime factors.
10. Find the sum of the cubes of first 10 natural numbers using the patterns of cubes.

AT A GLANCE

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¾ The cube of a number is the number raised to the power 3, i.e., if x is a number, then x is its cube where
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x = x × x × x.
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¾ A natural number n is a perfect cube, if n = m for some natural number m.
¾ The cube of an even natural number is even.

¾ The cube of an odd natural number is odd.
¾ The sum of the cubes of n-natural numbers is equal to the square of their sum, i.e.,
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2
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1 + 2 + 3 + ... + n = (1 + 2 + 3 + ... + n) .
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¾ A natural number x is said to be the cube root of a natural number y, if y = x , i.e., 3 y is the number
whose cube is x.
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¾ For any negative integer –a, -a 3 = - a 3 = -a.
¾ For any two integers x and y, xy = 3 x ¥ 3 y.
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p p 3 p
¾ For any rational number q , q π 0, 3 q = 3 q .

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