Answered

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.

Verified Answer :

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.

LucianoBordoli

Answer:

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

Step-by-step explanation:

The expression is :

\(\sqrt{32}+\sqrt{2}\)

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

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

\(\sqrt{32}+\sqrt{2}=\sqrt{(2).(16)}+\sqrt{2}=(\sqrt{2}).(\sqrt{16})+\sqrt{2}=\)

\((\sqrt{2}).(4)+\sqrt{2}=(5).(\sqrt{2})\)

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

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

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