Question

Simplify each expression, and classify the the result as rational or irrational.

Answer 1

1. Not rational

2. Rational

3. Not rational

4. Rational

5. Rational

6. Not rational

(had help from a calculator, nonetheless hope it helps :D)

Answer 2

Expressions $2\sqrt{5}-3\sqrt{5}$ , $\frac{\sqrt{42} }{\sqrt{68} }$ and $\sqrt{7}\pi-\sqrt{14}\pi$ are irrational.

Expressions $\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }$  and $\frac{\sqrt{64} }{32}$ are rational.

Rational and irrational expression :

The given expression are,

• $2\sqrt{5}-3\sqrt{5}=\sqrt{5}(2-3)=-\sqrt{5}$

           Which is irrational.

• $\frac{\sqrt{42} }{\sqrt{68} }=\frac{\sqrt{42} }{2\sqrt{17} }$

         Which is irrational.

• $\sqrt{5}(4\sqrt{5} -3\sqrt{5} )=5$

         Which is rational

•  $\frac{5\sqrt{3}-\sqrt{3} }{2\sqrt{3} }=2$

         Which is rational.

•  $\frac{\sqrt{64} }{32}=\frac{8}{32}=\frac{1}{7}$

          Which is rational.

• $\sqrt{7}\pi-\sqrt{14}\pi=\pi(\sqrt{7}-\sqrt{14} )$

          Which is irrational.

Learn more about the rational function here:

https://brainly.com/question/1851758