Question

An expression is shown below:

square root of 32 plus square root of 2

Which statement is true about the expression?

It is rational and equal to 4.
It is rational and equal to 5.
It is irrational and equal to 5 multiplied by square root of 2.
It is irrational and equal to 4 multiplied by square root of 2.

Answer 1

`√(32)+√(2)=√(16* 2)+√(2)=√(16)* √(2)+√(2)=4√(2)+√(2)=\boxed{5√(2)}`

The answer is "It is irrational and equal to 5 multiplied by square root of 2."

Answer 2

It is irrational and equal to
`5` multiplied by square root of
`2`

Explanation:

we have

`√(32)+√(2)`

Remember that

`32=2^(5)`

substitute in the expression

`\sqrt{2^(5)}+√(2)=4√(2)+√(2)=5√(2)`

therefore

It is irrational and equal to
`5` multiplied by square root of
`2`