Answer :

Given identity (a + b)2 = a2 + 2ab + b2

(i) (34)2


= (30+4)2


Here a = 30 and b = 4


= 302 +2× 30× 4 + 42


= 900 + 240 +16


= 1156


(ii)(10.2)2


= (10 +0.2)2


Using the given identity


Here a = 10, b = 0.2


= 102 + 2× 10 × 0.2 +(0.2)2


= 100 + 4 + 0.04


= 104.04


(iii) (53)2


= (50+3)2


Using the given identity


Here a = 50, b = 3


= (50)2 +2× 50 × 3 + 32


= 2500 + 300 +9


= 2809


(iv) (41)2


= (40+1) 2


Using the given identity


Here a = 40, b = 1


= 402 +2 × 40 × 1 + 12


= 1600 + 80 +1


= 1681


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