Find the squares of the following numbers: (I)527           (ii)   514             (iii)   525

Explanation

(i) `527=(500+27)`
`(a+b)^2=a^2+2ab+b^2`
`(500+27)^2=500^2+2times500times27+27^2`
`527^2=(250000+27000+729)`
`527^2=277729`

(ii) `514=(500+14)`
`(a+b)^2=a^2+2ab+b^2`
`(500+14)^2=500^2+2times500times14+14^2`
`514^2=(250000+14000+196)`
`514^2=264196`

(iii) `525=(500+25)`
`(a+b)^2=a^2+2ab+b^2`
`(500+25)^2=500^2+2times500times25+25^2`
`525^2=(250000+25000+625)`
`525^2=275625`