What is the square root of 306?
Understand the Problem
The question is asking for the square root of the number 306. To solve this, we will calculate the value that, when multiplied by itself, equals 306.
Answer
The square root of $306$ is approximately $17.492$.
Answer for screen readers
The square root of $306$ is approximately $17.492$.
Steps to Solve
- Identify the number to find the square root of
The number we need to find the square root of is $306$.
- Estimate the square root
Before calculating, we can estimate the square root of $306$. We know that $17^2 = 289$ and $18^2 = 324$. So, we can conclude: $$ 17 < \sqrt{306} < 18 $$
- Calculate the precise square root
To find the precise square root, we can use a calculator or a method such as the Newton-Raphson method if needed. For now, using a calculator gives: $$ \sqrt{306} \approx 17.492 $$
The square root of $306$ is approximately $17.492$.
More Information
The square root is a fundamental mathematical operation representing the value that, when multiplied by itself, gives the original number. The square root of $306$ is not a whole number, which is why we often refer to its approximate value in decimal format.
Tips
- A common mistake is to select estimates that are too far apart. Always ensure you're using perfect squares that are close to the target number to narrow down the possible range.
