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3.2 Open the folder downloaded from page vii for extra
questions of Mastery Q 3.2.
1. Determine whether each of the following numbers is a perfect cube. Explain how
you could support your answer by using the prime factorisation method.
(a) 128 (b) 343 (c) 1 000

2. CHAPTER

The prime factorisation of 3 375 is 3 × 3 × 3 × 5 × 5 × 5.
Explain how you could find the cube root of 3 375 by using the prime 3

factorisation method.

3. Find the value of each of the following without using a calculator.
1
4
(a) (−5) 3 (b) 1 2 3 (c) –1 1 2 3 (d) (–3.2) 3
5 6




3
3
3
3
(e) 125 (f) –512 (g) 729 (h) –27 000
8 64  
3
3
(i) 3 (j) 3 – (k) – 0.512 (l) 1.331
125 343
4. Calculate the value of each of the following using a calculator. Give your answers
correct to two decimal places for (e) to (h).
3
3
(a) 202 (b) (−17.6) (c) 0.041 3 (d) 1 –2 3 2 3
7


3
3
3
– 0.94
(e) 34.8 (f) 215.7 (g)  (h) 3 – 7
11
5. Estimate the value of each of the following:
3
3
3
3
(a) 2.9 (b) (–10.12) (c) 14.87 (d) (– 0.88)



3
3
3
(e) 65 (f) 344 (g) –728.9 (h) 3 8 1
8
6. The photo shows a decorative cubic box. The area of each
2
face of the box is 2 500 mm .
(a) Find the length, in mm, of the decorative box.
(b) Write the volume of the decorative box in cubic notation.
7. Find the value of each of the following:


3
3
2
2
(a) 8 + (– 0.3) (b) 4 × –125
1 2


3
3
(c) 36 ÷ 2 1 2 (d) 3 – 27 ÷ (–1)
2
2
2
7
1

3
(e) 5 × –216 ÷ 4 (f) 3 – 1 × 2 – 2
3
2
9 343 9
69
Squares, Square Roots, Cubes and Cube Roots
03 TB Math F1.indd 69 11/10/16 12:10 PM