QQuestionMathematics
QuestionMathematics
# Select the correct answer.
## Which number is an irrational number?
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve this problem step by step, following the precise LaTeX formatting guidelines you specified.
Step 2:: Understand Irrational Numbers
- Cannot be written as $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers
An irrational number is a real number that cannot be expressed as a simple fraction (ratio of two integers). Irrational numbers have decimal representations that: - Never terminate - Never repeat in a consistent pattern
Step 3:: Examine the Given Options
Let's analyze each number to determine which is irrational:
Step 4:\sqrt{4}
2. $$\sqrt{5}
Step 5:\sqrt{16}
4. $$\sqrt{25}
Step 6:: Evaluate Each Option
- $$\sqrt{25} = 5$$ (a rational number)
- \sqrt{5} (an irrational number)
Step 7:: Identify the Irrational Number
\sqrt{5}$$ is the only irrational number in this list because it cannot be simplified to a whole number and its decimal representation is non-terminating and non-repeating.
Final Answer
\sqrt{5} is the irrational number.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students