Question

Show that (5 + 3√2)^2 = 43 + 30√2.

Answer 1

foil the left side

Answer 2

exapnd lhs using (a+b)^2=a^2+b^2 +2ab

Answer 3

No don't FOIL, it will take a long time so, use the identity (a+b)^2=a^2+b^2+2ab on the left side

(5)^2+(3sqrt{2})^2+2(5)(3sqrt{2})=43+30sqrt{2}

Answer 4

Now solve the left side u will probably gt R.H.S.=L.H.S.

Answer 5

that's exactly what foil is though, expanding it

Answer 6

and it's easily done in this case! 5*5 + 5*3*sqrt(2) + 5*3*sqrt(2) + 3*3*sqrt(2)*sqrt(2) = 25 + 30*sqrt(2) + 18 = 43 + 30*sqrt(2)

Answer 7

Thank you so much! :)