Square Root Calculator
The square root of x is the non-negative number that multiplied by itself equals x.
Enter the number under the radical
Enter a non negative number to find its principal square root. The principal square root is the non negative value that squares back to the original number. For example, the principal square root of 9 is 3.
Use this page for decimal square roots, perfect square checks and quick math work. If you are solving an equation such as x^2 = 9, remember that the equation has two solutions, 3 and -3.
That extra equation step is easy to miss. The calculator evaluates a function, while an equation asks which values satisfy a statement.
Principal square root explained
The calculator result is the principal square root. It is not listing every number that can square to the input. This distinction causes a lot of confusion because square root notation and solving square equations are related but not identical.
For positive real inputs, the principal square root is non negative. For negative real inputs, a basic real number calculator cannot return a real square root.
How the root is checked
The square root of x is the principal value y such that y x y = x and y is not negative. Perfect squares have whole number roots, such as 25 giving 5.
Other values often produce decimals or simplified radicals. For school work, check whether the expected answer is decimal form, exact radical form or both.
Square root of 144
The square root of 49 is 7 because 7 x 7 = 49. The calculator returns 7, not -7, because the square root function returns the principal root.
If the equation is x^2 = 49, then both 7 and -7 work. That is an equation solving step, not the same as evaluating the square root symbol alone.
Negative numbers need a different tool
The biggest mistake is expecting the square root button to return both positive and negative values. The symbol returns the principal root.
Another mistake is entering a negative number into a real square root calculator. Negative square roots require complex numbers, such as i, which this basic page may not handle.
Also check whether the answer should be simplified. A decimal approximation may be useful, but an exact radical can be the expected school answer.
Square Root Calculator FAQ
Why does the square root calculator only show the positive answer?
Because the square root function returns the principal square root. For a positive real number, the principal root is the non negative root.
The negative value appears when you solve an equation like x^2 = 9. It is not returned by the square root symbol by itself.
Is the square root of 9 equal to 3 or plus and minus 3?
The square root of 9 is 3 when you evaluate the square root symbol. The equation x^2 = 9 has two solutions, 3 and -3.
Those statements are both useful, but they answer different questions.
If the page is evaluating sqrt(9), use 3. If the problem asks you to solve x^2 = 9, list both solutions.
Can I take the square root of a negative number?
Not as a real number. The real square root of a negative number is undefined. Complex numbers use i to handle these cases.
If your class has not introduced complex numbers, a negative input should usually be treated as outside the real domain.
What is a perfect square?
A perfect square is a number made by multiplying a whole number by itself. Examples include 1, 4, 9, 16, 25 and 36.
Perfect squares have whole number square roots. Non perfect squares usually have decimal or radical results.
Recognizing perfect squares helps you catch calculator entry mistakes quickly because the answer should be a clean whole number.
Should I use decimal form or radical form?
Use the format your problem asks for. Decimal form is useful for measuring and estimating. Radical form is exact and is often preferred in algebra.
For example, sqrt(2) as a decimal is rounded. The radical form sqrt(2) is exact.
If you are checking homework, look at the examples in the lesson. They usually show whether radicals should stay exact.
How can I check a square root result?
Square the result and see whether it returns the original input. If the calculator says sqrt(49) is 7, check 7 x 7. It gives 49.
For rounded decimal roots, the check may be close rather than exact. That is normal because the decimal was rounded.