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.e about the product square root of 2(5 + square root of 8)?

Answer 1

Hello,

√2*(5+√8)=5√2+4
Answer D

Answer 2

The answer is Irrational Number.

Explanation:

In order to determine the group of numbers, we have to use the properties of root.

The number is:

`√(2) *(5+√(8))\\(√(2)*5)+(√(2)*√(8))\\5*√(2) +√(16)\\5*√(2) +4`

Then, we have to know three definitions:

1. All rational numbers can be written as fractions equation, with a being an integer and b being a natural number.
2. Irrational numbers can not be written as fractions notation.
3. When a prime number is inside of a square root, the number is always a irrational.

Finally,
`5*√(2) +4` has a
`√(2)`, that it is a irrational number, therefore the addition is a irrational number too.