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 a rational number
A rational number is a number that can be expressed as a fraction $$\frac{p}{q}$$, where $$p$$ and $$q$$ are integers and $$q \neq 0$$.
Step 3:: Examine the square root of 58
\sqrt{58}$$ cannot be simplified to a simple fraction of integers.
Step 4:: Check if \sqrt{58} can be written as a ratio of integers
To do this, we need to determine if $$\sqrt{58}$$ is rational or irrational.
Step 5:: Proof by contradiction
However, 58 is not a perfect square, which means $$\sqrt{58}$$ cannot be rational.
Then it can be written as \frac{p}{q} in lowest terms. Squaring both sides:
Final Answer
It is an 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