What Is a Square Root?
A square root is a number that, when multiplied by itself, gives you the original number. For example, 8 × 8 = 64, so the square root of 64 is 8. In symbols, we write this as √64 = 8.
Every positive number has two square roots in algebra (one positive and one negative), but the symbol √ usually refers to the principal square root, which is the non-negative one. This calculator returns that principal value.
How to Use This Square Root Calculator
- Enter any number in the Number field.
- Choose how many decimal places you want for the result.
- Click Calculate Square Root (or press Enter).
- Read the output and verification line in the result box.
Examples
Example 1: Perfect square
Input: 81
Output: √81 = 9
Since the result is a whole number, 81 is a perfect square.
Example 2: Non-perfect square
Input: 2
Output: √2 ≈ 1.414214 (rounded)
This is an irrational number, so its decimal never ends or repeats.
Example 3: Decimal input
Input: 0.25
Output: √0.25 = 0.5
Square Root Rules You Should Know
- √(a × b) = √a × √b (for non-negative values)
- √(a / b) = √a / √b (for b > 0)
- (√a)2 = a
- √(x2) = |x|
Common Perfect Squares
- 1 → 1
- 4 → 2
- 9 → 3
- 16 → 4
- 25 → 5
- 36 → 6
- 49 → 7
- 64 → 8
- 81 → 9
- 100 → 10
Where Square Roots Are Used in Real Life
- Geometry: Finding side lengths and distances.
- Physics: Motion formulas and energy equations.
- Statistics: Standard deviation calculations.
- Finance: Volatility models and risk analysis.
- Engineering: Signal processing and structural analysis.
FAQ
Can I find the square root of a negative number?
In real numbers, no. The calculator will show that a negative value has no real square root. It also provides the complex-number form using i.
Why do I get a long decimal?
Many square roots are irrational, so their decimal expansion goes on forever. Use the decimal places field to control how much rounding you want.
What is a principal square root?
It is the non-negative square root. For example, both 5 and -5 square to 25, but √25 means 5.
Final Thoughts
A square root calculator saves time, reduces mistakes, and helps you understand number behavior quickly. Whether you are solving homework, working in data analysis, or checking engineering values, this tool gives fast and reliable results with customizable precision.