Math

Square Root Calculator

Roots and squares, with perfect-square neighbours.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Square root
Square root
—
Cube root
—
Square
—
Nearest perfect square below
—
Nearest perfect square above
—

Square Root Calculator by TheCalcTools

How the Square Root Calculator works

Enter any non-negative number.

The square root is the value that, multiplied by itself, gives your number.

Perfect squares on either side show where the root falls.

The formula

√x = x^(1/2)∛x = x^(1/3)

Worked example

Using the default values shown in the calculator:

Number50
  1. √50 = 7.0711; ∛50 = 3.6840.
  2. 50² = 2,500.00. Perfect squares around 50: 49 and 64.

Result:

Square root7.0711
Cube root3.6840
Square2,500.00
Nearest perfect square below49
Nearest perfect square above64

Frequently asked questions

How do I estimate a square root by hand?

Find the perfect squares on either side (49 and 64 for 50) and interpolate: √50 is a little over 7.

Why can't I enter a negative number?

Real square roots of negatives do not exist. They require imaginary numbers.

Sources and further reading

Nth Root CalculatorFind the nth root of a number, such as a square root or cube root Exponent CalculatorRaise any number to any power, and see the reciprocal and the equivalent root Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c² Percentage Change CalculatorFind the percentage change from an old value to a new value Ratio Simplifier CalculatorSimplify a ratio A : B to its lowest terms Fraction CalculatorDo arithmetic with two fractions and see the answer in lowest terms

More in Math · All calculators

This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.