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 step by step:
Step 2:: Understand the definition of rational and irrational numbers
- A rational number is a number that can be expressed as a fraction $$\frac{p}{q}$$ where $$p$$ and $$q$$ are integers and $$q \neq 0
- An irrational number cannot be expressed as a simple fraction of integers
Step 3:: Examine \sqrt{\frac{1}{9}}
- $$\sqrt{\frac{1}{9}} = \frac{1}{3}
- First, simplify inside the square root
Step 4:: Analyze the result
- $$\frac{1}{3}$$ is a rational number because:
* It can be expressed as a fraction of integers * Numerator (1) and denominator (3) are both integers * Denominator is not zero
Step 5:: Conclusion
- Since $$\sqrt{\frac{1}{9}} = \frac{1}{3}$$, which is a rational number
- The square root of \frac{1}{9} is rational
Final Answer
The square root of \frac{1}{9} is rational.
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