Question

classify the numbers as rational or irrational.
-7 √50 -7+√50 -7-√50
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, the sum or difference of a rational number and an irrational number is irrational, and the square root of a non - perfect square is irrational.

Step2: Classify - 7

• 7 can be written as $\frac{- 7}{1}$, where $-7$ and $1$ are integers and $1

eq0$. So, - 7 is a rational number.

Step3: Classify $\sqrt{50}$

We know that $50 = 25\times2$, so $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$. Since $\sqrt{2}$ is an irrational number (because 2 is not a perfect square), and multiplying a non - zero rational number (5) by an irrational number ($\sqrt{2}$) gives an irrational number. So, $\sqrt{50}$ is an irrational number.

Step4: Classify $-7+\sqrt{50}$

• 7 is a rational number and $\sqrt{50}$ is an irrational number. The sum of a rational number and an irrational number is irrational. So, $-7 + \sqrt{50}$ is an irrational number.

Step5: Classify $-7-\sqrt{50}$

• 7 is a rational number and $\sqrt{50}$ is an irrational number. The difference of a rational number and an irrational number (or equivalently, the sum of a rational number and the negative of an irrational number) is irrational. So, $-7-\sqrt{50}$ is an irrational number.

Answer:

rational: - 7
irrational: $\sqrt{50}$, $-7+\sqrt{50}$, $-7 - \sqrt{50}$