Square Root Calculator
Use this square root calculator to calculate the square root of any number, simplify square roots, check perfect squares, and see step-by-step explanations. This tool is helpful for students, parents, teachers, homework, algebra, geometry, and quick math checks.
Calculate a Square Root
Try an example:
Square Root Result
Common Square Roots Chart
| Number | Square Root | Perfect Square |
|---|---|---|
| 1 | 1 | Yes |
| 2 | 1.414 | No |
| 3 | 1.732 | No |
| 4 | 2 | Yes |
| 5 | 2.236 | No |
| 9 | 3 | Yes |
| 10 | 3.162 | No |
| 16 | 4 | Yes |
| 25 | 5 | Yes |
| 36 | 6 | Yes |
| 49 | 7 | Yes |
| 64 | 8 | Yes |
| 81 | 9 | Yes |
| 100 | 10 | Yes |
| 121 | 11 | Yes |
| 144 | 12 | Yes |
| 169 | 13 | Yes |
| 196 | 14 | Yes |
| 225 | 15 | Yes |
What Is a Square Root?
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8 because 8 × 8 = 64. This square root calculator helps you calculate square root values quickly and understand the square root of a number with clear steps.
How to Use the Square Root Calculator
- Enter a number in the calculator input box.
- Choose how many decimal places you want in the answer.
- Click the Calculate Square Root button.
- Review the decimal answer, simplified radical form, perfect square status, and step-by-step solution.
What Is a Perfect Square?
A perfect square is a number that has a whole number as its square root. Common perfect squares include 4, 9, 16, 25, 36, 49, 64, 81, and 100. This tool also works as a perfect square calculator because it checks whether your number has a whole-number square root.
How to Simplify Square Roots
To simplify a square root, find the largest perfect square factor of the number and move its square root outside the radical. For example, √50 = √25 × √2 = 5√2. Simplified radical form is useful for algebra, geometry, SAT prep, ACT prep, and homework.
Square Root Formula
The square root formula can be explained like this: if x² = n, then x is the square root of n. For example, if 7² = 49, then √49 = 7.
Square Root of Negative Numbers
The square root of a negative number is an imaginary number. For example, √-9 = 3i. The letter i is called the imaginary unit. This is common in algebra and advanced math.
Decimal Square Roots
Some square roots do not result in whole numbers. For example, √2 = 1.414213..., √3 = 1.732050..., and √5 = 2.236067.... This sqrt calculator lets you choose 2, 4, 6, or 10 decimal places.
Why Use This Square Root Calculator?
- Fast square root calculation
- Shows simplified radical form
- Shows decimal result
- Checks perfect squares
- Supports negative numbers and imaginary answers
- Gives step-by-step explanation
- Works on mobile, tablet, and desktop
- Helpful for students, teachers, parents, homework, algebra, and geometry
Square Root Examples
- √25 = 5
- √36 = 6
- √50 = 5√2
- √72 = 6√2
- √100 = 10
- √144 = 12
- √-16 = 4i
Frequently Asked Questions
What is a square root calculator?
A square root calculator is a tool that finds the square root of a number. It can show decimal answers, simplified radical forms, and step-by-step solutions.
What is the square root of 25?
The square root of 25 is 5 because 5 × 5 = 25.
What is the square root of 100?
The square root of 100 is 10 because 10 × 10 = 100.
What is the square root of 50?
The square root of 50 is approximately 7.071. In simplified radical form, √50 = 5√2.
How do you simplify square roots?
To simplify a square root, find the largest perfect square factor of the number and separate it from the radical. For example, √50 = √25 × √2 = 5√2.
What is a perfect square?
A perfect square is a number that has a whole number as its square root. For example, 36 is a perfect square because √36 = 6.
Can a square root be negative?
The principal square root of a positive number is not negative. However, equations like x² = 25 have two solutions: x = 5 and x = -5.
What is the square root of a negative number?
The square root of a negative number is an imaginary number. For example, √-9 = 3i.
Is this square root calculator free?
Yes, this calculator is free to use and works directly in your browser.