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Square Root Calculator

Calculate the square root, cube root, or any nth root of a number. Includes a perfect squares reference table.

Calculate Root

2√

Perfect Squares Reference (1–20)

1→1
2→4
3→9
4→16
5→25
6→36
7→49
8→64
9→81
10→100
11→121
12→144
13→169
14→196
15→225
16→256
17→289
18→324
19→361
20→400

How to Use This Tool

  1. Choose a root using the preset buttons (√ Square, ∛ Cube, ⁴√ 4th) or type any root value n into the "Root (n)" field.
  2. Enter the number x you want to find the root of in the "Number (x)" field.
  3. Read the result — the calculator instantly computes the nth root as you type.
  4. Check the verification line, which shows the result raised back to the power n to confirm it equals x.
  5. Look for the "Perfect Square/Cube/Power" badge, which appears when the result is a whole number.
  6. Use the Perfect Squares Reference table below to quickly look up squares of 1 through 20.

Formula & How It Works

Square Root

√x = x^(1/2)

The value that, when multiplied by itself, equals x.

Cube Root

∛x = x^(1/3)

The value that, when cubed (multiplied by itself three times), equals x.

nth Root

ⁿ√x = x^(1/n)

The value that, when raised to the power n, equals x. This calculator computes it as x raised to the power 1/n.

Negative Base Rule

ⁿ√(−x) is real only when n is odd

Even-order roots of negative numbers are not real; odd-order roots of negative numbers return a negative real result.

Practical Examples & Common Use Cases

Example: Square Root of 144

√144 = 144^(1/2) = 12, because 12 × 12 = 144.

Example: Cube Root of 27

∛27 = 27^(1/3) = 3, because 3 × 3 × 3 = 27.

Example: 4th Root of 81

⁴√81 = 81^(1/4) = 3, because 3 × 3 × 3 × 3 = 81.

Frequently Asked Questions

The square root of a number x is the value that, when multiplied by itself, gives x. For example, √49 = 7 because 7 × 7 = 49.

The nth root of x is x raised to the power of 1/n. For example, the 4th root of 81 = 81^(1/4) = 3.

Not in real numbers. The square root of a negative number is an imaginary number (e.g. √−1 = i). However, odd roots of negative numbers are real — for example, ∛−8 = −2.

A perfect square is an integer whose square root is also an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

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