1.

Find the squares of the given numbers by using simple calculations.(i) 52(ii) 105(iii) \(20\frac{1}{2}\)(iv) 10.2

Answer»

(i) 522 = (50 + 2)2

= 502 + 2 × 50 × 2 + 22

= 2500 + 200 + 4

= 2704

(ii) 1052 = (100 + 5)2

= 1002 + 2 × 100 × 5 + 52

= 10000 + 1000 + 25

= 11025

(iii) \((20\frac{1}{2})^2\) = \((20+\frac{1}{2})^2\)

= 202 + 2 × 20 × \(\frac{1}{2}\) + \((\frac{1}{2})^2\)

= 400 + 20 + \(\frac{1}{4}\)

= 420\(\frac{1}{4}\)

(iv) (10.2)2 = (10 + 0.2)2

= 102 + 2 × 10 × 0.2 + (0.2)2

= 100 + 4 + 0.04

= 104.04



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