square root of 306
Understand the Problem
The question is asking for the square root of 306, which is a mathematical operation that requires calculating the value that, when multiplied by itself, equals 306. We will solve it using step by step calculation.
Answer
17.4928557
Answer for screen readers
The square root of 306 is approximately 17.4928557
Steps to Solve
- Identify that the number is not a perfect square
306 is not a perfect square. This means its square root will be an irrational number.
- Use estimation to find a close approximation
Find two perfect squares between which 306 lies. For example, $17^2 = 289$ and $18^2 = 324$. So, $\sqrt{306}$ lies somewhere between 17 and 18.
- Refine the approximation using a calculator
Use a calculator to find a more accurate value. Plug in $\sqrt{306}$ into a calculator to get approximately 17.4928557. You can round this to a suitable number of decimal places as needed.
The square root of 306 is approximately 17.4928557
More Information
Square roots of non-perfect squares are irrational numbers, meaning they have non-repeating, non-terminating decimal expansions.
Tips
A common mistake is to assume the square root of a non-perfect square is a simple fraction. Always use a calculator for non-perfect squares.
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