Question

Simplify (2sqrt5 + 3sqrt7)^2?? I keep getting different answers every-time I try to solve. What steps do I do??

Answer 1

Show what you did?

Answer 2

Okay, since 2sqrt(5) and 3sqrt(7) are annoying, can you develop them so it would be only sqrt(#)?

Answer 3

E.g.: 2sqrt(5) could be expanded to sqrt(20)

Answer 4

3sqrt(7) = 42?

Answer 5

Nope, 3 = sqrt(9)
sqrt(9)*sqrt(7) = sqrt(63)

Answer 6

\[(\sqrt{20}+\sqrt{63})^2\]

Answer 7

Do something with it
Hint: \[(a+b)^2 = a^2+2ab+b^2\]

Answer 8

So sqrt(20) is A?

Answer 9

Yes.

Answer 10

{ sqrt(20) + sqrt(63)}^2 = sqrt(20)^2 + 2(20)(63) + (63)^2

Answer 11

Uh, you forgot some sqrt somewhere

Answer 12

{( 2sqrt(5) + 3sqrt(7)^2} = 83 + 12sqrt(35)

Answer 13

\[(\sqrt{20})^2+2(\sqrt{20}\sqrt{63})+(\sqrt{63})^2\]

Answer 14

So it would be 20 and 63 at both ends, since sqrt and ^2 cancels out
\[20 + 2\sqrt{20*63}+63\]

Answer should be pretty obvious now, simplify this and you'll get the answer.

Answer 15

83 + 12 sqrt(35)

Answer 16

wooot! :D