How to Solve Cube Root Using Calculator

What is a Cube Root?

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In mathematical terms, for a number \( x \), the cube root is written as \( \sqrt[3]{x} \).

For example, the cube root of 27 is 3 because \( 3 \times 3 \times 3 = 27 \). Cube roots are important in geometry for finding edge lengths of cubes and in algebra for solving cubic equations.

How to Use a Calculator for Cube Roots

Most scientific and graphing calculators have a dedicated cube root function. Here's how to use it:

1. Turn on your calculator and ensure it's in the appropriate mode (usually "DEG" or "RAD" for scientific calculators).
2. Enter the number you want to find the cube root of.
3. Press the cube root button (often labeled as \( \sqrt[3]{x} \) or with a cube root symbol).
4. Press the equals (=) button to display the result.

If your calculator doesn't have a dedicated cube root button, you can calculate it using the exponent function by raising the number to the power of 1/3.

Cube Root Formula

The cube root of a number \( x \) can be expressed using the following formula:

This formula states that the cube root of \( x \) is the number \( y \) that, when multiplied by itself three times, equals \( x \).

For negative numbers, the cube root is also negative. For example, \( \sqrt[3]{-8} = -2 \) because \( -2 \times -2 \times -2 = -8 \).

Worked Examples

Example 1: Positive Integer

Find the cube root of 64.

Solution:

1. We need to find a number \( y \) such that \( y \times y \times y = 64 \).
2. We know that \( 4 \times 4 \times 4 = 64 \).
3. Therefore, \( \sqrt[3]{64} = 4 \).

Example 2: Negative Integer

Find the cube root of -27.

Solution:

1. We need to find a number \( y \) such that \( y \times y \times y = -27 \).
2. We know that \( -3 \times -3 \times -3 = -27 \).
3. Therefore, \( \sqrt[3]{-27} = -3 \).

Example 3: Decimal Number

Find the cube root of 125.763.

Solution:

1. We need to find a number \( y \) such that \( y \times y \times y = 125.763 \).
2. We know that \( 5 \times 5 \times 5 = 125 \), but we need a more precise value.
3. Using a calculator, we find that \( 5.0156 \times 5.0156 \times 5.0156 \approx 125.763 \).
4. Therefore, \( \sqrt[3]{125.763} \approx 5.0156 \).

Common Mistakes

When calculating cube roots, several common mistakes can occur:

• Confusing cube roots with square roots: Remember that cube roots require three multiplications, while square roots require two.
• Incorrectly entering numbers: Ensure you enter the correct number before pressing the cube root button.
• Forgetting negative roots: Remember that negative numbers have negative cube roots.
• Rounding errors: For decimal numbers, be aware of potential rounding errors in the result.