Root Calculator
Calculate square roots, cube roots and any n-th root, with perfect-root detection. Get precise answers for any degree of root.
2 = square root, 3 = cube root, etc.
Root
12
2nd root of 144
Perfect root?
Perfect
Exact value 12
Check
144
Root raised to the power 2
A perfect root is one where the answer is an exact integer, such as the square root of 144 being 12. Even-indexed roots of negative numbers are not defined here.
How it works
n-th root = value^(1/n). A perfect root is an exact integer.
Example: √144 = 12 (perfect); √2 ≈ 1.4142 (not perfect).
Last updated: February 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
An electrician in Bengaluru checks that a 144 square centimetre cable cross-section is square. Entering 144 with degree 2 gives 12, because 12 times 12 is 144. For a storage box that needs a volume of 27 cubic centimetres, enter 27 with degree 3 to get 3, since 3 cubed is 27. The same tool handles higher degrees: the fourth root of 81 is 3, because 3 to the power 4 is 81. Non-perfect values such as the square root of 2 return a rounded decimal.
How to Use This Calculator
- Step 1: Enter the number you want the root of in the radicand field.
- Step 2: Enter the degree of the root: 2 for square, 3 for cube, or any other whole number.
- Step 3: Calculate the root and note whether the result is flagged as a perfect root.
- Step 4: Read the result, and use the perfect-root indicator to tell whether the answer is exact or rounded.
Worked Example
An electrician in Bengaluru checks that a 144 square centimetre cable cross-section is square. Entering 144 with degree 2 gives 12, because 12 times 12 is 144. For a storage box that needs a volume of 27 cubic centimetres, enter 27 with degree 3 to get 3, since 3 cubed is 27. The same tool handles higher degrees: the fourth root of 81 is 3, because 3 to the power 4 is 81. Non-perfect values such as the square root of 2 return a rounded decimal.
Tips and Common Mistakes
- •Tip 1: Even-degree roots of negative numbers are not real, so enter only non-negative radicands with degrees such as 2 or 4.
- •Tip 2: Odd-degree roots allow negative inputs; for example the cube root of -8 is -2.
- •Tip 3: Use the perfect-root flag when solving geometry problems where an exact value matters more than a decimal approximation.
- ✗Mistake 1: Confusing the degree with the radicand; entering 3 in the wrong field computes the square root of 3 instead of the cube root of your number.
- ✗Mistake 2: Rounding the output by hand before using it, since the calculator keeps far more precision than a quick handwritten estimate.
Frequently Asked Questions
What is a square root?
The square root of a number is the value that, multiplied by itself, gives the original number. The square root of 144 is 12 because 12 × 12 = 144.
What is an n-th root?
The n-th root of a number is the value that, raised to the power of n, gives the original number. The cube root of 27 is 3 because 3 × 3 × 3 = 27.
What is the square root of a negative number?
Negative numbers do not have real square roots — the answer is imaginary (i times the root of the absolute value). The calculator only returns real roots.
What is the difference between a square root and a cube root?
A square root is the value that squares to the number; a cube root is the value that cubes to it. The square root of 8 is about 2.83, but the cube root of 8 is exactly 2.
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