Find the square of the following numbers

(i) 32² =(30 + 2)²

= 30( 30 + 2) + 2(30 + 2)

=30² + 30 x 2 + 2 x 30 + 2²

=900+60+60+4

=1024

(ii)The number 35 has 5 in its unit's place. There  fore,

 35² = (3) (3 + 1)hundreds + 25

=(3 x 4) hundreds + 25

=1200 + 25 =1225

(iii)86²=(80 + 6)²

=80(80 + 6) + 6(80 + 6)

=80² + 80 x 6 + 6 x 80 + 6²

=6400 + 480 + 480 + 36

=7396

(iv) 93² = (90 + 3)²

=90(90 + 3) + 3(90 + 3)

=90² + 90 x 3 + 3 x 90 + 3²

=8100 + 270 + 270 + 9

=8649

(v)71² =(70 + 1)²

=70(70 + 1) + 1(70 + 1)

=70² + 70 x 1 + 1 x 70 + 1²

=4900 + 70 + 70 +1

=5041

(vi)46² = (40 + 6)²

=40(40 + 6) + 6(40 + 6)

=40² + 40 x 6 + 6 x 40 + 6²

=1600 + 240 + 240 + 36

=2116