Cal11 calculator
Search calculator...

How to Type Nth Root on Calculator

Reviewed by Calculator Editorial Team

Calculating nth roots is essential in mathematics, engineering, and science. This guide explains how to properly input nth root calculations on scientific calculators, including step-by-step instructions, formula explanations, and practical examples.

How to Type Nth Root on Calculator

The process of typing an nth root on a calculator varies slightly depending on the model, but follows these general steps:

Step 1: Enter the Radicand

First, type the number you want to find the root of (the radicand). For example, if you want to find the cube root of 27, type "27".

Step 2: Access the Root Function

Most scientific calculators have a dedicated root function. Look for a button labeled "x√y" or "y√x".

Step 3: Enter the Root Index

After pressing the root function button, enter the index (n) of the root you want to calculate. For a cube root, you would enter "3".

Step 4: Calculate the Result

Press the equals (=) button to calculate the result. The calculator will display the nth root of your original number.

Note: Some calculators may require you to use the exponent key (^) and fractions. For example, to find the cube root of 27, you might need to type "27^(1/3)".

Alternative Methods

If your calculator doesn't have a dedicated root function, you can use exponents and fractions:

  1. Type the radicand (e.g., 27)
  2. Press the exponent key (^)
  3. Type "1/" followed by the root index (e.g., 1/3)
  4. Press equals (=) to get the result

Nth Root Formula

The nth root of a number x is a number y such that y raised to the power of n equals x. Mathematically, this is represented as:

y = x^(1/n)

Where:

  • y = the nth root of x
  • x = the radicand (the number under the root)
  • n = the index of the root

For example, the cube root of 27 is 3 because 3³ = 27.

Worked Examples

Example 1: Square Root

Find the square root of 16.

  1. Type "16" on the calculator
  2. Press the "x√y" button
  3. Type "2" (for square root)
  4. Press equals (=)
  5. Result: 4 (since 4² = 16)

Example 2: Cube Root

Find the cube root of 64.

  1. Type "64" on the calculator
  2. Press the "x√y" button
  3. Type "3" (for cube root)
  4. Press equals (=)
  5. Result: 4 (since 4³ = 64)

Example 3: Fourth Root

Find the fourth root of 16.

  1. Type "16" on the calculator
  2. Press the "x√y" button
  3. Type "4" (for fourth root)
  4. Press equals (=)
  5. Result: 2 (since 2⁴ = 16)

FAQ

What is the difference between a square root and a cube root?

A square root is the number that, when multiplied by itself, gives the original number (x² = radicand). A cube root is the number that, when multiplied by itself three times, gives the original number (x³ = radicand).

How do I calculate an nth root on a basic calculator?

On basic calculators without a dedicated root function, you can use exponents and fractions. For example, to find the cube root of 27, type "27^(1/3)" and press equals.

What happens if I try to find the square root of a negative number?

Most calculators will display an error message because the square root of a negative number is not a real number. In mathematics, this is represented as an imaginary number (i√x).

Can I find the nth root of a fraction?

Yes, you can find the nth root of any positive real number, including fractions. Just enter the fraction as a decimal or in fraction form, then proceed with the root calculation.