Question

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

Answer 1

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 2

\[\sqrt{2}(5+\sqrt{8})\]

Answer 3

\[\sqrt2(5+\sqrt{8})=5\sqrt2+\sqrt16=4+5\sqrt2\]
We start by distributing the sqrt2 over the two terms in parentheses. The second term makes use of this property: \[\sqrt{xy}=\sqrt{x}\sqrt{y}\]. So, 2*8=16. We can then simplify the radical to 4 to get our answer. The answer is irrational because it contains sqrt2 still.

Answer 4

so then the answer is D?

Answer 5

@mslano

Answer 6

@hoblos

Answer 7

Yes, the answer is D.