(i) (4.9)2
(4.9)2 = (5 – 0.1)2
Substituting a = 5 and b = 0.1 in
(a – b)2 = a2 – 2ab + b2, we have
(5 – 0.1)2 = 52 – 2(5) (0.1) + (0.1)2
(4.9)2 = 25 – 1 + 0.01
= 24 + 0.01
(4.9)2 = 24.01
(ii) (100.1)2
(100.1)2 = (100 + 0.1)2
Substituting a = 100 and b = 0.1 in
(a + b)2 = a2 + 2ab + b2, we have
(100 + 0.1)2 = (100)2 + 2(100) (0.1) + (0.1)2
(100.1)2 = 10000 + 20 + 0.01
(100.1)2 = 10020.01
(iii) (1.9) x (2.1)
(1.9) x (2.1) = (2 – 0.1) x (2 + 0.1)
Substituting a = 100 and b = 0.1 in
(a – b) (a + b) = a2 – b2 we have
(2 – 0.1) (2 + 0.1) = 22 – (0.1)2
(1.9) x (2.1) = 4 – 0.01
(1.9) (2.1) = 3.99
