Question

classify the numbers as rational or irrational. \\(\sqrt{8}\\) \\(4\\) \\(\sqrt{8} - 4\\) \\(\sqrt{8} + 4\\) \
rational \
irrational

Explanation:

Step1: Define rational/irrational numbers

Rational numbers can be written as $\frac{p}{q}$ where $p,q$ are integers, $q
eq0$; irrational numbers cannot.

Step2: Analyze $\sqrt{8}$

$\sqrt{8}=2\sqrt{2}$, $\sqrt{2}$ is irrational, so $\sqrt{8}$ is irrational.

Step3: Analyze 4

4 can be written as $\frac{4}{1}$, so it is rational.

Step4: Analyze $\sqrt{8}-4$

Subtracting a rational number (4) from an irrational number ($\sqrt{8}$) results in an irrational number.

Step5: Analyze $\sqrt{8}+4$

Adding a rational number (4) to an irrational number ($\sqrt{8}$) results in an irrational number.

Answer:

Rational: 4
Irrational: $\sqrt{8}$, $\sqrt{8}-4$, $\sqrt{8}+4$