Square Root Calculator

How to use √ square root and cube root functions

Overview

Root extraction is the inverse operation of exponentiation, used to find the root of a number.

  • sqrt (square root): Find the second root of a number, √x
  • cbrt (cube root): Find the third root of a number, ∛x

Root operations are widely used in geometry, physics, and engineering, such as calculating hypotenuse length and standard deviation.

Syntax

sqrt(value) // Calculate square root
cbrt(value) // Calculate cube root
value^(1/2) // Alternative way to calculate square root
value^(1/3) // Alternative way to calculate cube root

Examples

Example 1: Calculate √16
Input: sqrt(16)
Result: 4
Because 4² = 16
Example 2: Calculate √2
Input: sqrt(2)
Result: 1.414213...
√2 is an irrational number, approximately 1.414
Example 3: Calculate ∛27
Input: cbrt(27)
Result: 3
Because 3³ = 27
Example 4: Calculate ∛(-8)
Input: cbrt(-8)
Result: -2
Cube root can handle negative numbers because (-2)³ = -8
Example 5: Using exponent for roots
Input: 81^(1/4)
Result: 3
Calculate the fourth root of 81
Example 6: Pythagorean theorem
Input: sqrt(3^2 + 4^2)
Result: 5
When legs are 3 and 4, hypotenuse is 5

Important Notes

  1. Square root sqrt() only accepts non-negative numbers; negative square roots are undefined in real numbers
  2. Cube root cbrt() can accept negative numbers
  3. sqrt(x) is equivalent to x^(1/2)
  4. For any nth root, use the form x^(1/n)

Related Topics

Exponents & Powers Absolute Value