Square Root Calculator — Calculate √x and nth Roots
Calculate the square root, cube root, or any nth root of a number. Also shows whether the number is a perfect square or cube. See also Exponent Calculator and Log Calculator.
2 = square root, 3 = cube root, etc.
How to Calculate Square Roots
The square root of a number x is the value that, when multiplied by itself, gives x. For example, √144 = 12 because 12 × 12 = 144. This calculator also handles nth roots: the cube root (3rd root), 4th root, and beyond. Enter your number and the root degree, then click Calculate. The calculator will also tell you whether the number is a perfect square, cube, or nth power.
Square Root Formula
√x = x^(1/2)
∛x = x^(1/3)
ⁿ√x = x^(1/n)
Properties:
√(a × b) = √a × √b
√(a / b) = √a / √b
(√x)² = x
Example
√144 = ?
We need a number that multiplied by itself gives 144.
12 × 12 = 144 ✓
√144 = 12 (perfect square)
Frequently Asked Questions
What is a perfect square?
A perfect square is an integer that is the square of another integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. The square root of a perfect square is always a whole number.
Can you take the square root of a negative number?
Not in real numbers. The square root of a negative number is an imaginary number. For example, √(-1) = i (the imaginary unit). However, odd roots of negative numbers are real: ∛(-8) = -2.
What is the difference between square root and cube root?
A square root finds a number that multiplied by itself gives the original (2nd root). A cube root finds a number that multiplied by itself three times gives the original (3rd root). For example, √9 = 3 and ∛27 = 3.