Question

An expression is shown below:

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

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.