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

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.

Answer 2

For this case we have the following product:

`√(2)(5+√(8))`

Applying the distributive property we have:

`5√(2)+√(2)√(8)`

Then, rewriting the expression we have:

`2√(2)√(2)+5√(2)`

`4+5√(2)`

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

Answer:

`4+5√(2)`

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