Taking 3rd Root on Standard Calculator

Calculating cube roots on a standard calculator requires a few simple steps. This guide explains how to find the cube root of any number using basic calculator functions.

How to Calculate Cube Roots

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Standard calculators don't have a dedicated cube root function, but you can calculate it using exponentiation. Here's how:

Step-by-Step Guide

Enter the number you want to find the cube root of.
Press the exponentiation button (usually marked as "xʸ" or "^").
Enter the exponent value of 1/3 (for cube root).
Press the equals button (=) to get the result.

Note: Some calculators may use a different notation for exponents. If your calculator doesn't have an exponent button, look for a function like "y√x" and enter 3 for the root value.

The Formula

The cube root of a number x can be calculated using the exponentiation formula:

∛x = x^(1/3)

This formula works for both positive and negative numbers. For example, ∛(-8) = -2 because (-2) × (-2) × (-2) = -8.

Worked Examples

Example 1: Finding ∛64

Enter 64 on your calculator.
Press the exponentiation button (xʸ).
Enter 1/3.
Press = to get 4.

Verification: 4 × 4 × 4 = 64

Example 2: Finding ∛-27

Enter -27 on your calculator.
Press the exponentiation button (xʸ).
Enter 1/3.
Press = to get -3.

Verification: (-3) × (-3) × (-3) = -27

Cube Root Comparison Table
Number	Cube Root	Verification
1	1	1 × 1 × 1 = 1
8	2	2 × 2 × 2 = 8
27	3	3 × 3 × 3 = 27
64	4	4 × 4 × 4 = 64
125	5	5 × 5 × 5 = 125

Frequently Asked Questions

Can I find cube roots without a calculator?: Yes, you can estimate cube roots by trial and error or use the Newton-Raphson method for more precise results.
What's the difference between square roots and cube roots?: Square roots find a number that, when multiplied by itself twice, equals the original number. Cube roots find a number that, when multiplied by itself three times, equals the original number.
Can I find cube roots of negative numbers?: Yes, the cube root of a negative number is negative. For example, ∛(-27) = -3.
Why is the cube root important in real life?: Cube roots are used in geometry to find edge lengths of cubes, in physics for volume calculations, and in engineering for material science applications.
What if my calculator doesn't have an exponent button?: Look for a function like "y√x" and enter 3 for the root value, then the number you want to find the cube root of.