Question

1 Find the square of the following numbers without actual multiplication
a) 19 b) 23 c) 45 d) 52​

Answer 1

Answer:

for the following sums we must use the two algebraic identities:

(a+b)^2 = a^2 + b^2 +2ab

(a-b)^2 = a^2 + b^2 -2ab

a) 19 is nothing but 20 - 1

So,

19^2 = (20-1)^2

Using the identity, (a-b)^2 = a^2 + b^2 -2ab

(20-1)^2 = 400 + 1 - 40

=361

b) similarly, 23 is (20+3)

23^2 = (20+3)^2

using the identity (a+b)^2 = a^2 + b^2 +2ab

(20+3)^2 = 400 + 9 + 120

=529

c) 45 = ( 50 - 5)

(50-5)^2 = 2500 + 25 - 500

=2025

d)52 = (50+2)

(50+2)^2 = 2500 + 4 + 200

=2704

Hope this helped.