Question

Find the squares of the following numbers :
(i) 127 (ii) 503
(iii) 451 (iv) 862
(v) 265

Answer 1

$\left(i\right)(127{)}^2=(120+7{)}^2\left\{\right(a+b{)}^2=a^2+2ab+b^2\}=(120{)}^2+2\times 120\times 7+(7{)}^2=14400+1680+49=16129$

$\left(ii\right)(503{)}^2=(500+3{)}^2\left\{\right(a+b{)}^2=a^2+2ab+b^2\}=(500{)}^2+2\times 500\times 3+(3{)}^2=250000+3000+9=253009$

$\left(iii\right)(451{)}^2=(400+51{)}^2\left\{\right(a+b{)}^2=a^2+2ab+b^2\}=(400{)}^2+2\times 400\times 51+(51{)}^2=160000+40800+2601=203401$

$\left(iv\right)(862{)}^2=(800+62{)}^2\left\{\right(a+b{)}^2=a^2+2ab+b^2\}=(800{)}^2+2\times 800\times 62+(62{)}^2=640000+99200+3844=743044$

$\left(v\right)(265{)}^2\left\{\right(a+b{)}^2=a^2+2ab+b^2\}=(200+65{)}^2=(200{)}^2+2\times 200\times 65+(65{)}^2=40000+26000+4225=70225$