Page 70 - Maths Skills - 8

68 Maths

6. The volume of a cubical box is 4096 cubic metres. Find the length of each side of the box.

7. Find the cube roots of the following.
(i) – 9261 (ii) – 3375 (iii) – 4096 (iv) – 5832
8. Find the smallest number by which 4394 must be divided to make the quotient a perfect cube. Also, find
the cube root of the quotient.

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3
9. Find the value of 0 027. 0 008. .
10. Find the cube roots of the following.
(i) 0.001 (ii) 0.085184 (iii) 2.197 (iv) 4.096

ASSESSMENT TIME

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COMPETENCY BASED QUESTIONS 4. The cube root of – m is ________.
5. If m and n are two integers, then 3 mn
A. Multiple-Choice Questions
________ × ________ .
1. The cube root of x is denoted by:
(i) x (ii) 3 x C. Write ‘T’ for true and ‘F’ for false statements
(iii) both (i) & (ii) (iv) none of these 1. 125 is a perfect cube.

2. For a natural number p, if p = q, then q is 2. The cube root of – a is – a.
3
3
called a
(i) perfect square (ii) perfect cube 3. 11 is the cube root of – 1331.
(iii) both (i) & (ii) (iv) none of these 4. If p p 3 p 1

3. The cube of a negative integer is q is a rational number, then 3 q 3 q
(i) positive (ii) negative
(iii) any of these (iv) none of these
4. The cube of an even natural number is 5. For two integers a and b, we have

(i) odd (ii) even 3 ab 3 a ÷ 1 .
3 b
(iii) both (i) & (ii) (iv) none of these
5. If m is a non-zero number, then the cube of m is D. Case Study Based Questions

(i) m 2 (ii) m We have any positive integers a . –a is a negative
(iii) m × m (iv) none of these integer such that—
2
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B. Fill in the Blanks (–a) = (–a) × (–a) × (–a) = –(a) 3
1. The cube of an odd natural number is ________. 3 a 3 a 3 a 3

2. The cube of a rational number p is . Thus, the cube root of a negative perfect cube is
q ________ negative of the cube root of its absolute value.
3. If a = b , where a is a natural number, then b is In other words, to find the cube root of a negative
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the ________ of a. perfect cube, we find the cube root of its absolute
value and multiply it by –1.