Question

Which statement is true about the product square root of 2(5 + square root of 8)?

It is rational and equal to 7.

It is rational and equal to 9.

It is irrational and equal to 4 + square root of 10.

It is irrational and equal to 4 + 5square root of 2.

Answer 1

@texaschic101

Answer 2

\[\sqrt2(5+\sqrt8) = 5\sqrt2 + \sqrt8\sqrt2 = 5\sqrt2 + \sqrt{16} = 5\sqrt2 + 4\]

Answer 3

I used the following identities:
\[
a(b+c) = ab + ac\\
\sqrt{a}\sqrt{b} = \sqrt{ab}
\]

Answer 4

but whats the awnser? @JoelSjogren