Is square root of 81 a rational number?
Understand the Problem
The question is asking whether the square root of 81 is a rational number. A rational number is one that can be expressed as a fraction of two integers. Since the square root of 81 is a whole number, we will determine if it meets that criterion.
Answer
The square root of 81 is a rational number, specifically $9$.
Answer for screen readers
The square root of 81 is a rational number, specifically $9$.
Steps to Solve
- Calculate the Square Root of 81
To determine if the square root of 81 is a rational number, we first need to calculate it.
The square root is defined as a number that, when multiplied by itself, gives the original number:
$$ \sqrt{81} = x \quad \text{where} \quad x \cdot x = 81 $$
- Evaluate the Square Root
Finding the square root of 81:
$$ \sqrt{81} = 9 $$
- Check for Rationality
Next, we need to check if 9 is a rational number. A rational number can be expressed as a fraction of two integers.
9 can be expressed as:
$$ \frac{9}{1} $$
Since both 9 and 1 are integers, 9 is indeed a rational number.
The square root of 81 is a rational number, specifically $9$.
More Information
The square root of 81, which is $9$, is a perfect square. Perfect squares have integer square roots and are always rational numbers.
Tips
- Assuming that square roots of all numbers are irrational: Only non-perfect squares have irrational square roots. Always check if the number is a perfect square.
