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 + 5 square root of 2.

Answer 1

It is irrational since the square root sign in the answer is present.

Explanation:

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

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

Explanation:

`√(2)(5+√(8))=5√(2)+√(2\cdot 8)=5√(2)+√(16)\\\\=4+5√(2)`

The square root of 2 in the result makes the result irrational.