Third Root Microsoft Calculator

Microsoft Calculator provides a built-in function for calculating the third root of a number. This guide explains how to use this feature, understand the underlying formula, and interpret the results.

How to Use the Third Root Function in Microsoft Calculator

Calculating the third root in Microsoft Calculator is straightforward. Here's a step-by-step guide:

Open the Calculator app on your Windows device.
Switch to the Scientific view by clicking the "Scientific" button at the top of the calculator.
Enter the number you want to find the third root of.
Click the "x³" button to calculate the cube of the number.
Click the "1/x" button to calculate the reciprocal of the cube.
The result displayed is the third root of your original number.

Note

Microsoft Calculator does not have a direct "third root" button, but you can calculate it using the cube and reciprocal functions as shown above.

The Formula for Calculating the Third Root

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

Third Root Formula

∛x = x^(1/3)

This formula states that the third root of x is equal to x raised to the power of one-third.

For example, the third root of 27 is 3 because 3 × 3 × 3 = 27.

Worked Examples

Example 1: Calculating the Third Root of 8

Using the formula:

Calculation

∛8 = 8^(1/3) = 2

Verification: 2 × 2 × 2 = 8, which confirms our calculation.

Example 2: Calculating the Third Root of 216

Using the formula:

Calculation

∛216 = 216^(1/3) = 6

Verification: 6 × 6 × 6 = 216, which confirms our calculation.

Example 3: Calculating the Third Root of 0.125

Using the formula:

Calculation

∛0.125 = 0.125^(1/3) = 0.5

Verification: 0.5 × 0.5 × 0.5 = 0.125, which confirms our calculation.

Frequently Asked Questions

What is the difference between the square root and the third root?

The square root of a number x is a value that, when multiplied by itself, gives x. The third root is a value that, when multiplied by itself three times, gives x. In mathematical terms, √x = x^(1/2) and ∛x = x^(1/3).

Can I calculate the third root of a negative number in Microsoft Calculator?

Yes, you can calculate the third root of a negative number. For example, the third root of -8 is -2 because (-2) × (-2) × (-2) = -8.

What happens if I try to calculate the third root of zero?

The third root of zero is zero because 0 × 0 × 0 = 0.

Is there a direct third root button in Microsoft Calculator?

No, Microsoft Calculator does not have a direct third root button. You can calculate the third root using the cube and reciprocal functions as described in this guide.