How to use it
- Choose root or exponent mode.
- Enter the number.
- Enter the root index or exponent, or tap a quick button.
- Read the result and copy it.
Roots and powers
The square root of x is the number that gives x when multiplied by itself: √144 = 12 because 12 × 12 = 144. The cube root works with three factors (∛27 = 3), and in general the nth root of x is the number whose nth power is x.
In exponent mode the calculator raises a number to any power, including negative and fractional exponents. Results are shown with up to 10 decimal places and can be copied with one click. Everything is calculated in your browser.
Examples
| Input | Result |
|---|---|
| √144 | 12 |
| √72 | 8.4852813742 (= 6√2) |
| ∛27 | 3 |
| ∛−8 | −2 |
| 4th root of 16 | 2 |
| 2^10 | 1,024 |
| 2^−1 | 0.5 |
| 9^0.5 | 3 |
Odd roots of negative numbers are real (∛−8 = −2), but even roots of negative numbers are not real numbers, so the calculator says so instead of returning a value.
Simplifying square roots
For whole numbers, the calculator also writes the square root in simplest radical form: it pulls out the largest perfect-square factor.
Example: √72 = √(36 × 2) = 6√2.
Others: √50 = 5√2, √48 = 4√3, √200 = 10√2. If the number is a perfect square, it says so: √169 = 13 because 13 · 13 = 169. Perfect squares worth knowing: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
Exponent rules
- x^0 = 1 (for x ≠ 0)
- x^−n = 1 / x^n, so 2^−3 = 1/8 = 0.125
- x^(1/n) = nth root of x, so 27^(1/3) = 3
- x^(m/n) = (nth root of x)^m, so 8^(2/3) = 4
- x^a · x^b = x^(a+b)
A negative base with a fractional exponent, such as (−8)^0.5, is not a real number, and the calculator reports that.
Everyday uses
- Diagonal of a room or screen: a 10 ft × 12 ft room has a diagonal of √(10² + 12²) = √244 ≈ 15.62 ft. The triangle calculator solves these with all the details.
- Side of a square from its area: a 400 sq ft square patio is √400 = 20 ft on each side.
- Growth rates: if an investment doubled in 6 years, its yearly growth factor is the 6th root of 2 ≈ 1.1225, about 12.2% a year.
- Edge of a cube from its volume: a 27 cubic foot cube has 3-foot edges.
For more functions in one place, use the scientific calculator.
Common mistakes
- Adding under a root. √(9 + 16) = √25 = 5, but √9 + √16 = 7. Roots do not split over addition.
- Forgetting the negative root. x² = 49 has two solutions, 7 and −7, even though √49 means the positive root 7.
- Negative bases and powers. −3² = −9, but (−3)² = 9. Use parentheses in exponent mode.
- Rounding too early. Keep full precision until the last step, then round once.
- Mixing up roots and division. The cube root of 27 is 3, not 9 (27 / 3). A root undoes a power, not a multiplication.
- Assuming every square root is irrational. √144 is exactly 12; only non-perfect squares such as √2 have endless decimals.
Frequently asked questions
How do I find a square root?
Enter the number and keep the index at 2. The calculator shows the decimal value and, for whole numbers, the simplified radical.
What is the square root of 72 in simplest form?
6√2, because 72 = 36 × 2 and √36 = 6.
Can I take the cube root of a negative number?
Yes. Odd roots of negative numbers are real, for example ∛−8 = −2.
Why is there no square root of a negative number?
No real number multiplied by itself gives a negative result. The answer exists only among complex numbers.
What does a fractional exponent mean?
x^(1/n) is the nth root of x, so 16^0.5 = 4 and 27^(1/3) = 3.
Last updated: November 12, 2026