Question

classify the numbers as rational or irrational. \\(sqrt{50}\\) \\(5\\) \\(sqrt{50}+5\\) \\(sqrt{50}-5\\) rational irrational

Explanation:

Step1: Recall definitions

A rational number is a number that can be expressed as $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. An irrational number is a non - repeating, non - terminating decimal and cannot be expressed as a fraction of two integers. Also, if $a$ is rational and $b$ is irrational, then $a + b$ and $a - b$ are irrational.

Step2: Analyze $\sqrt{50}$

Simplify $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$. Since $\sqrt{2}$ is irrational, $5\sqrt{2}$ (which is $\sqrt{50}$) is irrational.

Step3: Analyze $5$

The number $5$ can be written as $\frac{5}{1}$, where $p = 5$ and $q=1$ are integers with $q
eq0$. So, $5$ is rational.

Step4: Analyze $\sqrt{50}+5$

We know that $\sqrt{50}$ is irrational (from Step 2) and $5$ is rational (from Step 3). The sum of a rational number and an irrational number is irrational. So, $\sqrt{50}+5$ is irrational.

Step5: Analyze $\sqrt{50}-5$

We know that $\sqrt{50}$ is irrational (from Step 2) and $5$ is rational (from Step 3). The difference of a rational number and an irrational number (or vice - versa) is irrational. So, $\sqrt{50}-5$ is irrational.

Answer:

• Rational: $5$
• Irrational: $\sqrt{50}$, $\sqrt{50}+5$, $\sqrt{50}-5$