2.2.1 Squares, Square Roots, Cube and Cube Roots, PT3 Practice 1


2.2.1 Squares, Square Roots, Cube and Cube Roots, PT3 Practice 1

Question 1:
Calculate the values of the following:
(a) 50 98 (b) 1 17 64 (c) 81 0.01 (d) 3.24  

Solution:
(a) 50 98 = 50 25 98 49 = 25 49 = 5 7

(b) 1 17 64 = 81 64 = 9 8 = 1 1 8

(c) 81 0.01 = 9 1 100 = 9 1 10 = 9 0.1 = 8.9

(d) 3.24 = 3 24 100 = 3 6 25 = 81 25 = 9 5 = 1 4 5



Question 2:
Calculate the values of the following:
(a) 16 250 3 (b) 4 256 3 (c) 0.008 3 (d) 0.729 3   

Solution:
(a) 16 250 3 = 8 125 3 = 2 5

(b) 4 256 3 = 1 64 3 = 1 4

(c) 0.008 3 = 8 1000 3 = 2 10 = 0.2

(d) 0.729 3 = 729 1000 3 = 9 10 = 0.9



Question 3:
Find the value of 3 3 8 3 + 2 14 25 .  

Solution:
3 3 8 3 + 2 14 25 = 27 8 3 + 64 25 = 3 2 + 8 5 = 31 10 = 3 1 10



Question 4:
Find the values of the following:
  (a) 1 – (–0.3)3.
  (b) ( 2.1 ÷ 27 3 ) 2  

Solution:
(a)
1 – (–0.3)3 = 1 – [(–0.3) × (–0.3) × (–0.3)]
  = 1 – (–0.027)
  = 1 + 0.027
  = 1.027

(b)
( 2.1 ÷ 27 3 ) 2 = ( 2.1 ÷ 3 ) 2 = ( 0.7 ) 2 = 0.49



Question 5:
Find the values of the following:
(a) ( 9 + 8 3 ) 2 (b) 144 ÷ 216 3 × 0.3 3  

Solution:
(a) ( 9 + 8 3 ) 2 = [ 9 + ( 2 ) ] 2 = 7 2 = 49

(b) 144 ÷ 216 3 × 0.3 3 = 144 ÷ 6 × ( 0.3 × 0.3 × 0.3 ) = 24 × 0.027 = 0.648


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