Square Root Calculator
Find the square root, cube root, or any nth root of a number — with simplified radical form for whole-number radicands.
What is Square Root Calculator?
The square root calculator finds √n, ∛n (cube root), or any nth root of a number. For perfect squares it returns a clean integer; for others it gives the decimal expansion plus the simplified radical form (when applicable).
Formula
The nth root of x is the number r such that rn = x.
- n = 2 → square root (√)
- n = 3 → cube root (∛)
- n = 4, 5, … → fourth root, fifth root, etc.
Even roots of negative numbers are undefined in real numbers. Odd roots of negatives are negative: ∛(−27) = −3.
Worked example
√72 = 8.485…
Simplified radical: 72 = 36 × 2, so √72 = 6√2.
∛125 = 5 (perfect cube).
How to use this calculator
- Enter the number whose root you want.
- Set the root index — 2 for square root, 3 for cube root, n for nth root.
- The decimal value, simplified radical (where applicable), and perfect-root flag update instantly.
Frequently asked questions
What's a "simplified radical"?
√72 simplifies to 6√2 because 72 = 36 × 2, and √36 = 6. Pulling out perfect-square factors gives a cleaner form. The calculator does this automatically for square roots of whole numbers.
Why is the square root of a negative number undefined?
In the real numbers, no number squared gives a negative result. Square roots of negatives exist in the complex number system as imaginary numbers (√−1 = i), but most U.S. K–12 math stops at real numbers.
Cube root of negative numbers?
Defined and real. ∛(−8) = −2 because (−2)³ = −8. Any odd root of a negative number is negative.
How accurate is the result?
Up to 8 decimal places — enough for any high-school or early-college math, including SAT/ACT problems.