Question

I need help simplifying (2(square root of 5)+3(square root of 7)^2

Answer 1

\[\left(2\sqrt{5}+3\sqrt{7}\right)^2\]??

Answer 2

\[(2\sqrt{5}+3\sqrt{7})(2\sqrt{5}+3\sqrt{7})\] is a start, then do the usual four multiplications, sometimes denoted as "first, outer, inner, last" and you get
\[2\sqrt{5}\times 2\sqrt{5}+2\sqrt{5}\times 3\sqrt{7}+2\sqrt{5}\times 3\sqrt{7}+3\sqrt{7}\times 3\sqrt{7}\]

Answer 3

first term is \(4\times 5=20\) middle terms add up to \(6\sqrt{35}+6\sqrt{35}=12\sqrt{35}\) and the last one is \(9\times 7=63\)

Answer 4

when you add it all up you get
\[83+12\sqrt{35}\]