🔥 We are adding new calculators, Feel free to submit your feature request to hello@measuremetics.com Thank you.

Nth Root Calculator

Calculate the nth root of any number, including fractional exponents.

How to Use Nth Root Calculator

This calculator computes the nth root of a number.

  1. Enter Number: Enter the number for which you want to calculate the root.
  2. Enter Root: Enter the value of 'n' (the root). For square root, enter 2. For cube root, enter 3, and so on.
  3. Calculate: Click the "Calculate" button to compute the nth root.
  4. View Result: The calculated nth root will be displayed.

Fractional Exponents: To calculate fractional exponents like x(a/b), enter b/a as the root. For example, to calculate x(2/3), you should enter 1.5 (which is 3/2) in the root field. This is because x(2/3) = x(1/1.5).

Negative Numbers and Even Roots: Calculating even roots of negative numbers is not possible within real numbers. The calculator will display an error message.

What is an Nth Root

The nth root of a number is a value that, when raised to the power of n, gives you back the original number. Think of it as "what number do I need to multiply by itself n times to get this result?"

Simple Examples

Square Root (2nd root)

  • √16 = 4 because 4 × 4 = 16
  • The square root asks: "What number times itself equals 16?"

Cube Root (3rd root)

  • ∛8 = 2 because 2 × 2 × 2 = 8
  • The cube root asks: "What number times itself three times equals 8?"

How to Calculate Nth Roots

Basic Method

  • Identify your number (let's call it x)
  • Identify which root you want (let's call it n)
  • Use this formula: x^(1/n)

Examples with Steps

Finding the 4th root of 16:

  • Number (x) = 16
  • Root (n) = 4
  • Question: "What number multiplied by itself 4 times gives 16?"
  • Calculate: 16^(1/4) = 2
  • Verify: 2 × 2 × 2 × 2 = 16

Finding the 3rd root of 27:

  • Number (x) = 27
  • Root (n) = 3
  • Question: "What number multiplied by itself 3 times gives 27?"
  • Calculate: 27^(1/3) = 3
  • Verify: 3 × 3 × 3 = 27

Working with Fractional Exponents

Let's say you want to calculate x^(2/3):

First, understand what this means:

  • Take the cube root (∛x)
  • Then square the result

In the calculator:

  • Enter your number (x)
  • For the root, enter 1.5 (which is 3/2)
  • This works because x^(2/3) = x^(1/1.5)

Important Tips

When using even roots (2nd, 4th, 6th, etc.):

  • Positive numbers always work
  • Negative numbers won't give real answers

When using odd roots (3rd, 5th, 7th, etc.):

  • Both positive and negative numbers work
  • The answer keeps the same sign as the original number

For decimal answers:

  • Always check by raising your answer to the nth power
  • It should give you back your original number

Remember: You can always check your answer by multiplying it by itself n times - you should get back to your original number!