What is the square root of 69?
Understand the Problem
The question is asking for the square root of the number 69, which is a mathematical concept. To solve this, we will find the number that, when multiplied by itself, gives 69.
Answer
The square root of 69 is approximately $8.3066$.
Answer for screen readers
The square root of 69 is approximately $8.3066$.
Steps to Solve
- Identify the square root concept
The square root of a number $x$ is a value $y$ such that $y^2 = x$. For this problem, we are looking for a number $y$ such that $y^2 = 69$.
- Set up the equation
We can express the problem using an equation:
$$ y = \sqrt{69} $$
- Approximate the square root
To find an approximation for $\sqrt{69}$, we can find two perfect squares between which 69 lies.
We know that:
$$ 8^2 = 64 $$
and
$$ 9^2 = 81 $$
This tells us that:
$$ 8 < \sqrt{69} < 9 $$
- Use a calculator for more precision
Using a calculator, we can find a more precise value:
$$ \sqrt{69} \approx 8.3066 $$
The square root of 69 is approximately $8.3066$.
More Information
The square root of a number is important in various fields, including geometry, physics, and statistics. Understanding square roots lays the groundwork for more advanced mathematical concepts such as quadratic equations and functions.
Tips
- Misunderstanding the square root definition: Some people might confuse square roots with squares. Remember, the square root is the number that, when multiplied by itself, equals the original number.
- Estimating inaccurately: Always check the perfect squares around the number you’re estimating the square root of to get a better initial approximation.
