How to Square Root by 3 on Calculator

Calculating cube roots is a fundamental math operation that finds the number which, when multiplied by itself three times, gives the original number. This guide explains how to perform cube root calculations using a calculator, including step-by-step instructions, practical examples, and a built-in calculator tool.

What is a cube root?

The cube root of a number x is a value y such that y × y × y = x. In mathematical terms, this is written as y = ∛x. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Cube roots are used in various mathematical and real-world applications, including:

Volume calculations in geometry
Solving cubic equations in algebra
Physics calculations involving three-dimensional measurements
Financial modeling and investment growth calculations

Cube Root Formula

For any real number x, the cube root can be expressed as:

∛x = x^(1/3)

How to calculate cube roots

There are several methods to calculate cube roots:

Using a calculator: Most scientific calculators have a cube root function (often labeled as "x³" or "³√x").
Prime factorization: Break down the number into its prime factors and group them in sets of three.
Estimation method: Use known cube roots to estimate the value.
Newton's method: An iterative numerical approach for more precise calculations.

Note

For most practical purposes, using a calculator is the simplest and most accurate method.

Using a calculator for cube roots

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

Enter the number you want to find the cube root of
Press the cube root function button (often labeled as "³√x" or "x³")
Press the equals (=) button to get the result

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

Example Calculation

To find the cube root of 64:

Enter 64 on your calculator
Press the exponent button (often labeled as "yˣ")
Enter 1/3
Press equals to get the result: 4

Examples of cube roots

Here are some common cube root examples:

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

For non-perfect cubes, the cube root will be an irrational number. For example, the cube root of 2 is approximately 1.2599.

Frequently Asked Questions

What is the difference between square root and cube root?

The square root of a number x is a value y such that y × y = x, while the cube root is a value y such that y × y × y = x. In other words, the square root is the second root, and the cube root is the third root.

Can I calculate cube roots of negative numbers?

Yes, you can calculate cube roots of negative numbers. For example, the cube root of -8 is -2 because (-2) × (-2) × (-2) = -8. This is different from square roots, which are only defined for non-negative numbers in real numbers.

How accurate are calculator cube root calculations?

Most scientific calculators provide cube root calculations with high precision, typically to at least 10 decimal places. For most practical purposes, this level of accuracy is sufficient.

Where are cube roots used in real life?

Cube roots are used in various fields including:

Engineering for volume calculations
Physics for three-dimensional measurements
Finance for investment growth calculations
Computer graphics for 3D modeling