Square Root Calculator
Calculate the square root, cube root, or any nth root of a number. Includes a perfect squares reference table.
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Perfect Squares Reference (1–20)
Square Roots & nth Roots
Square Root (√x) — The number that, when multiplied by itself, equals x. Example: √144 = 12 because 12² = 144.
Cube Root (∛x) — The number that, when cubed, equals x. Example: ∛27 = 3 because 3³ = 27.
nth Root (ⁿ√x) — The number that, when raised to the power n, equals x. Calculated as x^(1/n).
Perfect Squares — Numbers whose square root is a whole integer (e.g. 1, 4, 9, 16, 25 …).
Negative numbers: Even-order roots (2nd, 4th…) of negative numbers are not real. Odd-order roots (3rd, 5th…) of negative numbers are negative real numbers.
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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