Root Calculator (Square, Cube, and n-th Root)
Use this tool to calculate roots quickly. Enter a number and the root degree (n). Example: number 81 and degree 4 gives 3.
- Square root: x = 49, n = 2 → 7
- Cube root: x = 27, n = 3 → 3
- Negative odd root: x = -125, n = 3 → -5
What does “root” mean in a calculator?
In math, a root is the inverse of a power. If a number r raised to the power n equals x, then r is the n-th root of x. A calculator helps you find this value instantly.
If rn = x, then r = x1/n
Most common roots people use
1) Square root (√x)
The square root is the most common root. It answers: “What number multiplied by itself gives x?” Example: √36 = 6, because 6 × 6 = 36.
2) Cube root (∛x)
The cube root answers: “What number multiplied by itself three times gives x?” Example: ∛64 = 4, because 4 × 4 × 4 = 64.
3) n-th root
This is the general version. You choose any degree n: fourth root, fifth root, tenth root, and so on.
How to do roots on different calculators
Standard/basic calculator
- Many basic calculators only have a square root key: √.
- If you need other roots, use exponent form when available: x^(1/n).
- If no exponent key exists, use an online root calculator (like above).
Scientific calculator
- For square root: press √, then the number.
- For n-th root: enter number, then power key (^ or y^x), then (1 ÷ n).
- Example: 81^(1/4) = 3.
Phone calculator apps
- Rotate to landscape on many phones to open scientific mode.
- Use √ for square root and xy for fractional exponents.
- For cube root of 125: enter 125^(1/3).
Important rule for negative numbers
Negative inputs need special care:
- Odd roots of negative numbers are real numbers (example: ∛(-8) = -2).
- Even roots of negative numbers are not real in standard arithmetic (example: √(-9) is not a real number).
This page’s calculator follows that exact rule and explains errors clearly when input is invalid.
Quick practice examples
| Number (x) | Degree (n) | Root | Check |
|---|---|---|---|
| 16 | 2 | 4 | 4² = 16 |
| 32 | 5 | 2 | 2⁵ = 32 |
| 0.008 | 3 | 0.2 | 0.2³ = 0.008 |
| -343 | 3 | -7 | (-7)³ = -343 |
Common mistakes (and how to avoid them)
- Using n = 0 — undefined. A “0th root” does not exist.
- Typing 1/n wrong — always use parentheses:
1/5, not just1then/5in a separate operation. - Ignoring sign rules — even roots of negative values are not real.
- Rounding too early — keep extra decimals during intermediate steps for better accuracy.
FAQ: root in calculator
How do I type cube root if there is no ∛ button?
Use exponent form: x^(1/3).
Can I calculate 4th or 7th root?
Yes. Use x^(1/4) or x^(1/7), or enter n directly in the calculator above.
Why does my calculator show error for √(-9)?
Because square roots of negative numbers are not real values in regular real-number mode.
Final takeaway
Once you remember the identity x^(1/n), roots become easy on any calculator. Use square root for daily problems, cube root for volumes, and n-th roots for advanced math, finance, and science tasks. Keep this page bookmarked when you need fast, accurate root calculations.