Perfect square
√144 = 12 because 12² = 144 and the principal root is nonnegative.
Find a principal square root
Square root calculator
Calculate the square root of a nonnegative number and see how to interpret and check the result.
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Formula and steps included
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Formula
What a square root means
Principal square root: √n = x when x² = n and x ≥ 0
A square root reverses squaring. The principal square root symbol refers to the nonnegative value whose square equals the original number.
Perfect squares have whole-number roots. Other nonnegative values usually produce irrational roots, so their decimal display is an approximation at the shown precision.
How to use the formula
Check the input domain
For a real-number result, the number under the square root must be zero or positive.
Look for a perfect-square factor
Recognizing factors such as 4, 9, 16, or 25 can help simplify a radical exactly.
Calculate the principal root
Use the nonnegative root when the radical symbol appears without a plus-or-minus sign.
Square the answer to check
Multiplying the root by itself should return the original number, allowing for displayed decimal rounding.
Worked examples
Square root calculator examples
Non-perfect square
√50 = √(25 × 2) = 5√2, which is approximately 7.071067812.
Common questions
Square root calculator FAQ
Why does a positive number have two solutions when squared?
Both x and −x have the same square, but the radical symbol √n means only the nonnegative principal square root. An equation such as x² = 9 has solutions x = 3 and x = −3.
Can I take the square root of a negative number?
Not within the real numbers. Negative radicands require complex numbers, using i where i² = −1.
Why is a square-root answer sometimes rounded?
Roots of non-perfect squares are often irrational decimals that never terminate or repeat, so a numeric display must show a finite approximation.
Is the number I enter private?
Your number is not saved by default or uploaded. You can opt into Remember on this device or download a local JSON backup.