Square Root Calculator Online
Use our free square root calculator to calculate the square root of any non-negative number instantly. Get accurate decimal answers, exact forms, simplified radicals, verification and step-by-step calculations.
Whether you are solving a math problem, checking homework, studying algebra or verifying a calculation, this sqrt calculator makes square root calculations quick and easy.
Square Root Calculator
Calculate square roots online
Quick Examples
Tap to useSquare Root Result
Your calculated square root and supporting details.
Ready to calculate
Enter a non-negative number above and calculate its square root.
Simplified radical form when applicable.
Calculate Square Roots Online
A square root calculator helps you find the number that produces a given value when multiplied by itself. For example, the square root of 25 is 5 because 5 × 5 = 25.
This free online square root calculator provides more than a decimal answer. Depending on the number you enter, it can show an exact form, simplified radical form, verification information and calculation steps.
You can use the calculator for school mathematics, algebra, geometry, homework, exam preparation, mathematical research, engineering calculations and everyday number checking.
How to Use the Square Root Calculator
Calculate a square root in a few simple steps.
Enter a Number
Enter any non-negative whole number or decimal.
Calculate
Select Calculate to process the square root.
View Your Answer
See the decimal and exact square root results.
Check the Steps
Review verification and the calculation details.
Square Root Formula
Understanding the basic mathematical relationship.
The square root of a number is the value that produces the original number when multiplied by itself. The symbol √ is called the radical sign.
Common Perfect Squares
These numbers have whole-number square roots.
Exact Form vs Decimal Form
Some square roots cannot be represented as a simple whole number. An exact radical form can preserve the mathematical value.
Exact radical notation keeps the mathematical value in simplified form without rounding.
Decimal form provides a convenient numerical approximation that is useful for practical calculations.
How to Simplify a Square Root
Simplifying a radical means taking perfect-square factors outside the radical sign.
Because 36 is a perfect square and √36 = 6, the factor 6 can be moved outside the radical. Therefore, √72 simplifies to 6√2.
When to Use a Square Root Calculator
School & Homework
Check algebra, geometry and arithmetic calculations.
Geometry
Calculate values used in distance and geometric formulas.
Algebra
Check square roots and radical expressions while solving equations.
Quick Verification
Quickly verify a square root without manual calculation.
Everything You Need for Square Root Calculations
Accurate Square Roots
Calculate square roots quickly with precise numerical results.
Decimal Answers
Get useful decimal approximations for non-perfect squares.
Verification
Check the result by relating the answer back to the original number.
Step-by-Step
Review useful calculation details to better understand the result.
Important Information About Square Roots
The principal square root of a positive number is normally taken as the non-negative value.
Perfect squares have integer square roots, such as 4, 9, 16, 25 and 100.
Many numbers have irrational square roots, meaning their decimal expansion does not terminate or repeat.
Negative numbers do not have real square roots. This calculator is designed for real-number square roots.
Square Root Examples
Frequently Asked Questions
What is a square root?
A square root is a number that produces the original number when multiplied by itself. For example, 5 × 5 = 25, so √25 = 5.
What is the square root of 72?
The square root of 72 is approximately 8.4852813742. Its simplified exact form is 6√2.
What is a perfect square?
A perfect square is a number whose principal square root is an integer. Examples include 1, 4, 9, 16, 25 and 100.
Can I calculate the square root of a decimal?
Yes. Enter a decimal number such as 123.45 and the calculator will provide its square root as a decimal approximation.
Can I calculate a negative square root?
Negative numbers do not have real square roots. This calculator works with real-number square roots and therefore accepts non-negative values.
What is the difference between an exact and decimal answer?
An exact answer preserves the mathematical value, often using radical notation such as 6√2. A decimal answer provides a numerical approximation such as 8.4853.
Who can use this square root calculator?
Students, teachers, parents, professionals and anyone who needs a quick way to calculate or verify a square root can use it.
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