2.2.3 Squares, Square Roots, Cube and Cube Roots, PT3 Practice


Question 10:
(a) Find the value of  0.09 (b) Calculate the value of  ( 5 7 × 49 ) 2

Solution:
(a) 0.09 = 9 100 = 3 10 =0.3 (b) ( 5 7 × 49 ) 2 = ( 5 7 × 7 ) 2                   = 5 2                   =25


Question 11:
(a) Find the value of  1 27 3 (b) Calculate the value of  ( 7+ 8 3 ) 2

Solution:
(a)  1 27 3 = 1 3 × 1 3 × 1 3 3 = 1 3 (b) ( 7+ 8 3 ) 2 = [ 7+( 2 ) ] 2                  = 5 2                  =25


Question 12:
(a) Find the value of  ( 1 4 ) 3 . (b) Calculate the value of  ( 4.2÷ 27 3 ) 2 .

Solution:
(a) ( 1 4 ) 3 = 1 4 × 1 4 × 1 4            = 1 64 (b) ( 4.2÷ 27 3 ) 2 = ( 4.2÷3 ) 2                     = 1.4 2                     =1.4×1.4                     =1.96


Question 13:
(a) Find the value of  0.008 3 . (b) Calculate the value of  3 2 × 64 27 3 .

Solution:
(a)  0.008 3 = 8 1000 3            = 2 10            =0.2 (b)  3 2 × 64 27 3 = 9 3 × 4 3                 =12


Question 14:
(a) Find the value of  ( 3 4 ) 3 . (b) Calculate the value of  2 10 27 3 ÷( 2 2 3 2 ).

Solution:
(a)  ( 3 4 ) 3 = 3 4 × 3 4 × 3 4            = 27 64 (b)  2 10 27 3 ÷( 2 2 3 2 )= 64 27 3 ÷( 49 )                            = 4 3 ÷5                            = 4 3 × 1 5                            = 4 15

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