Question

Find the square of the following numbers.

1) $32$

2) $35$

3) $71$

4) $46$

Answer 1

Solution:

1) 32 can be written as $(30+2)$

$32²=(30+2)²$=(30+2)(30+2)

we know the identity

$(a+b)²=a²+b²+2ab$

$={30}^2+2\times 30\times 2+2^2$= $900+120+4=1024$

$\left(32\right)²=1024$

2) $(35{)}^2$ = $(30+5{)}^2$= ${30}^2$+$2\times 30$ x 5 $+5²$= 900 + 300 + 25 = $1225$

$(35{)}^2=1225$

3) $71²$ = (70 + 1)²= 70² + 2 X 70 X 1 + 1²= 4900 + 140 + 1 = $5040+1$ = $5041$

${71}^2=5041$

4) ${46}^2$ =(40+6)²= 40²+ 2 X 40 X 6 +6²= $1600+480+36=2080+36=2116$

${46}^2$=2116