Question

Find the square of the following numbers without actual multiplication
1)67²
2)44²
3)29²

Answer 1

1) 67 can be written as 70-3

therefore

(67)^2 = (70-3)^2

Using the formula of (a-b)^2= a^2-2ab+b^2

(70-3)^2= 4900-(2×70×3)+9

= 4900-420+9

=4489

2) 44 can be written as 40+4

Using the formula (a+b)^2=a^2+2ab+b^2

(40+4)^2= 1600+(2×40×4)+16

= 1600+320+16

=1936

3) 29 can be written as 30-1

Using the formula of (a-b)^2=a^2-2ab+b^2

(30-1)^2= 900-(2×30×1)+1

= 900-60+1

= 841