Square Root & Nth Root Calculator

Calculator Inputs

Select operation and enter values.

Index
Radicand

Result

Computed value based on inputs.

Math Rules

The n-th root of a number x is a number r which, when raised to the power n, yields x.

Root & Radical Guide

How to Use

  1. 1Enter the number (Radicand) you want to find the root of.
  2. 2Enter the Nth root degree (e.g., 2 for square root, 3 for cube root).
  3. 3Click calculate to find the root value.

Formula & Logic

Finding the nth root is the inverse operation of raising a number to the nth power. It asks 'what number multiplied by itself n times gives me x?'

x= Radicand (Number inside symbol)
n= Index or Degree (The root)
r= Root value

Practical Applications

1

Geometry

Find the side length of a square given its area (square root) or a cube given its volume (cube root).

2

Statistics

Calculate Standard Deviation, which involves taking the square root of the Variance.

3

Physics

Used in Root Mean Square (RMS) calculations for AC voltage and current.

Frequently Asked Questions

QCan I find the square root of a negative number?

For real numbers, no. The square root of a negative number is an imaginary number (involving i). This calculator currently supports real number roots.

QWhat is a Perfect Square?

A perfect square is a number that has an integer as its square root (e.g., 4, 9, 16, 25).

QIs calculating roots the same as fractional exponents?

Yes! calculating the nth root of x is mathematically identical to raising x to the power of 1/n.