Square Root Calculator
Calculate the square root or any nth root of a number.
About the Square Root Calculator
Square roots and higher-degree roots (cube roots, fourth roots, and beyond) come up throughout algebra, geometry, and physics. This calculator finds the root of any degree for any positive number, defaulting to a standard square root when the degree is left at 2.
How It Works
The calculator raises the number you enter to the power of one divided by the root degree, which is mathematically equivalent to taking that root — the same identity used internally by virtually every calculator and computer.
Root = Number^(1/degree). For a square root, degree = 2; for a cube root, degree = 3.
Example
Scenario: Finding the square root of 144.
Result: 12, since 12 × 12 = 144.
Assumptions & Limitations
- For even-degree roots (square root, fourth root, etc.), assumes the number entered is non-negative, since even roots of negative numbers are not real numbers.
- Odd-degree roots (like cube roots) of negative numbers are mathematically valid and handled correctly.
- Returns only the principal (positive) root for even-degree roots, not the negative counterpart, which is also technically a valid root.
Frequently Asked Questions
What is the difference between a square root and a cube root?
A square root asks what number multiplied by itself gives the target (degree 2), while a cube root asks what number multiplied by itself three times gives the target (degree 3) — set the root degree field accordingly.
Can I find the square root of a negative number?
Not as a real number — the square root of a negative number is only defined in the complex number system, which this calculator does not compute; however, odd-degree roots like cube roots of negative numbers work normally.
Why does 144 have two square roots, 12 and -12?
Both 12×12 and (-12)×(-12) equal 144, so mathematically both are valid square roots, though this calculator reports the principal positive root, which is the standard convention.