How to Plug in Cubed Root in Calculator

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

What is a Cubed Root?

The cubed root of a number x is a value that, when multiplied by itself three times, gives the original number. Mathematically, it's represented as:

∛x = y, where y × y × y = x

For example, the cubed root of 27 is 3 because 3 × 3 × 3 = 27. Cubed roots are important in geometry for finding edge lengths of cubes, in physics for volume calculations, and in algebra for solving cubic equations.

How to Calculate Cubed Root

Calculating cubed roots manually requires understanding of exponents and repeated multiplication. For most practical purposes, using a calculator is more efficient. Here's how to do it properly:

Identify the number you want to find the cubed root of.
Enter the number into your calculator.
Press the cubed root function (often labeled as "x³" or "³√x").
Read the result displayed on the calculator screen.

Note: Not all calculators have a dedicated cubed root function. In such cases, you can calculate it as x^(1/3) using the exponent function.

Calculator Methods

Different calculators have different ways to input cubed roots. Here are common methods:

Calculator Type	Input Method
Scientific Calculator	Press the "³√x" button or use the exponent function with 1/3
Graphing Calculator	Use the "cube root" function or enter x^(1/3)
Programmable Calculator	Write a custom program or use the built-in cube root function
Online Calculator	Look for the "cube root" option in the function menu

Examples

Let's look at some practical examples of cubed roots:

Number	Cubed Root	Verification
8	2	2 × 2 × 2 = 8
27	3	3 × 3 × 3 = 27
64	4	4 × 4 × 4 = 64
125	5	5 × 5 × 5 = 125

These examples show how cubed roots can be used to find the edge length of a cube when you know its volume.

FAQ

What is the difference between square root and cubed root?

A square root finds a number that, when multiplied by itself twice, equals the original number. A cubed root finds a number that, when multiplied by itself three times, equals the original number.

Can I calculate cubed roots of negative numbers?

Yes, in real numbers, negative numbers have real cubed roots. For example, the cubed root of -8 is -2 because (-2) × (-2) × (-2) = -8.

How do I calculate cubed roots without a calculator?

You can use the binomial approximation method or trial and error with multiplication tables, but this is time-consuming and less precise than using a calculator.