Question

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

Answer 1

For this case we have the following product:

$\sqrt{2}(5+\sqrt{8})$

Applying the distributive property we have:

$5\sqrt{2}+\sqrt{2}\sqrt{8}$

Then, rewriting the expression we have:

$2\sqrt{2}\sqrt{2}+5\sqrt{2}$

$4+5\sqrt{2}$

We note that the answer is a irrational number, because the square root of two is not an exact number.

Answer:

$4+5\sqrt{2}$

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

Answer 2

We are given with two factors: square root of 2 and 5 + square root of 8. We use a scientific calculator that displays irrational answers. The product of the two factors is 4 + 5 square root of 2. The answer is irrational since the square root sign in the answer is present.