Simplify the following expressions: `(i)\ (sqrt(3)+\ sqrt(7))^2` `(ii)\ (sqrt(5)-sqrt(3))^2` `(iii)\ (2sqrt(5)+3sqrt(2))^2`

Explanation

(i) `(sqrt(3)+\ sqrt(7))^2`
we know,
`(a+b)^2=a^2+b^2+2ab`
`(sqrt(3)+sqrt(7))^2=(sqrt(3))^2+(sqrt(7))^2+2xxsqrt3xxsqrt7`
`=3+7+2sqrt21=10+2sqrt21`
(ii) `(sqrt(5)-sqrt(3))^2`
we know,
`(a-b)^2=a^2+b^2-2ab`
`(sqrt(5)-sqrt(3))^2=(sqrt(5))^2+(sqrt(3))^2-2xxsqrt5xxsqrt3`
`=5+3-2sqrt15=8-2sqrt15`
(iii) `(2sqrt(5)+3sqrt(2))^2`
we know,
`(a+b)^2=a^2+b^2+2ab`
`(2sqrt(5)+3sqrt(2))^2=(2sqrt(5))^2+(3sqrt(2))^2+2xx2sqrt5xx3sqrt2`
`=20+18+12sqrt10=38+12sqrt10`