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

7.07106781186 would answer the first part. The second part would be that 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:

The expression is :

`√(32)+√(2)`

We can write that
`32=(2).(16)`

If we replace this in the expression we can distribute the square root :

`√(32)+√(2)=√((2).(16))+√(2)=(√(2)).(√(16))+√(2)=`

`(√(2)).(4)+√(2)=(5).(√(2))`

The expression is equal to 5 multiplied by square root of 2.

Given that
`√(2)` is an irrational number, meaning that it can't be expressed as a quotient of two integer numbers, the result
`(5).(√(2))` will be an irrational number.