Question

Find the squares of the following numbers without actual multiplication:
$49$, $52$

• A. $2441;2704$
• B. $2401;2784$
• C. $2401;2704$
• D. $2441;2784$

Answer 1

The correct option is C $2401;2704$

${49}^2=(40+9{)}^2=40(40+9)+9(40+9)$
$=(40{)}^2+40\times 9+9\times 40+9^2$
$=1600+360+360+81$
So, ${49}^2=2401$
${52}^2=(50+2{)}^2=50(50+2)+2(50+2)$
$={50}^2+50\times 2+2\times 50+2^2$
$=2500+100+100+4$
So, ${52}^2=2704$.