How To Find A Cubed Root On A Calculator

Easily calculate the cubed root of any number and understand how to find it on a calculator.

Find the Cubed Root

Common Cubed Roots

Table of common numbers and their cubed roots, with calculator input guidance.

Number (x)	Cubed Root (∛x)	How to find on a calculator
1	1	1^(1/3) or ∛1
8	2	8^(1/3) or ∛8
27	3	27^(1/3) or ∛27
64	4	64^(1/3) or ∛64
125	5	125^(1/3) or ∛125
1000	10	1000^(1/3) or ∛1000
-1	-1	(-1)^(1/3) or ∛(-1)
-8	-2	(-8)^(1/3) or ∛(-8)
-27	-3	(-27)^(1/3) or ∛(-27)
0	0	0^(1/3) or ∛0

What is a Cubed Root?

A cubed root of a number ‘x’ is a value which, when multiplied by itself three times, equals ‘x’. For example, the cubed root of 8 is 2 because 2 × 2 × 2 = 8. The symbol for the cubed root is ∛, so we write ∛8 = 2. It can also be expressed as raising the number to the power of 1/3, like 8^1/3 = 2.

Unlike square roots, you can find the cubed root of any real number, including negative numbers. For instance, the cubed root of -27 is -3 because (-3) × (-3) × (-3) = -27.

Who should use it?

Finding the cubed root is useful in various fields, including mathematics, physics, engineering, and even finance. Anyone needing to reverse a cubing operation (x³) or solve equations involving cubes will need to find the cubed root. It’s fundamental in geometry when dealing with volumes of cubes and spheres.

Common Misconceptions

• Cubed root vs. dividing by 3: The cubed root of a number is NOT the same as dividing the number by 3 (e.g., ∛27 = 3, but 27/3 = 9).
• Only for positive numbers: While the principal square root is defined only for non-negative numbers in real numbers, the cubed root is defined for all real numbers.

Cubed Root Formula and Mathematical Explanation

The cubed root of a number x is denoted as ∛x or x^1/3. If y = ∛x, then it means:

y × y × y = x

or

y³ = x

To find the cubed root, you are looking for the number that, when cubed, gives the original number. For perfect cubes (like 1, 8, 27, 64…), the cubed root is an integer. For other numbers, the cubed root is often an irrational number.

Variables Table

Variable	Meaning	Unit	Typical Range
x	The number whose cubed root is being found	Depends on context (e.g., m^3 if volume)	Any real number (-∞ to +∞)
y or ∛x	The cubed root of x	Depends on context (e.g., m)	Any real number (-∞ to +∞)

How to Find a Cubed Root on a Calculator

Finding the cubed root on a calculator depends on the type of calculator you have:

1. Basic Calculator

Most basic calculators do not have a direct cubed root button. You might not be able to find it directly unless it has a power function.

2. Scientific Calculator (Physical or App)

Scientific calculators usually offer a few ways to find the cubed root:

• Dedicated Cubed Root Button (∛x or x^1/3): Some calculators have a button specifically for the cubed root. You would typically enter the number, then press this button. It might be a secondary function, requiring you to press ‘SHIFT’ or ‘2nd’ first.
• x^y, y^x, or ^ Button: Most scientific calculators have a power button. To find the cubed root of x, you raise x to the power of 1/3 (which is approximately 0.33333333). So, you would enter the number (x), press the power button (x^y), enter (1/3) or 0.333333333, and then press ‘=’. For 1/3, you might need parentheses: `x ^ ( 1 / 3 ) =`.
• x^1/y Button: Some calculators have a button for the y-th root of x. To find the cubed root, you’d enter the number x, press the x^1/y button (or its SHIFT/2nd function), enter 3, then press ‘=’.

3. Online Calculator (like this one)

Our calculator above allows you to simply enter the number and get the cubed root instantly.

Practical Examples (Real-World Use Cases)

Example 1: Volume of a Cube

Imagine you have a cube-shaped box with a volume of 343 cubic centimeters (cm³). To find the length of one side (s) of the cube, you need to find the cubed root of the volume, since Volume = s³.

• Number (Volume): 343 cm³
• Cubed Root (Side length): ∛343 = 7 cm
• Interpretation: Each side of the cube is 7 cm long.

Example 2: Scaling Dimensions

If you want to create a scale model of an object and the model needs to have 1/8th the volume of the original, the linear dimensions (length, width, height) of the model will be scaled down by a factor of ∛(1/8).

• Volume Ratio: 1/8 = 0.125
• Scaling Factor for dimensions: ∛0.125 = 0.5
• Interpretation: The model’s dimensions should be half those of the original to achieve 1/8th the volume. Finding the cubed root is key here.

How to Use This Cubed Root Calculator

1. Enter the Number: Type the number for which you want to find the cubed root into the “Enter a Number” field. You can enter positive or negative numbers.
2. Calculate: The calculator will automatically update the result as you type, or you can click the “Calculate” button.
3. View Results:
   • Primary Result: Shows the calculated cubed root.
   • Original Number Display: Confirms the number you entered.
   • Verification Result: Shows the cubed root multiplied by itself three times, which should be very close to your original number (allowing for minor rounding).
4. Reset: Click “Reset” to clear the input and results, returning to the default value.
5. Copy Results: Click “Copy Results” to copy the main result and intermediate values to your clipboard.

This tool simplifies finding the cubed root without needing a physical scientific calculator.

Key Factors That Affect Cubed Root Results

1. The Number Itself: The magnitude and sign of the number directly determine the cubed root. Larger positive numbers have larger positive cubed roots; negative numbers have negative cubed roots.
2. Sign of the Number: The cubed root of a positive number is positive, and the cubed root of a negative number is negative (∛-8 = -2).
3. Perfect Cubes: If the number is a perfect cube (like 8, 27, -64), the cubed root will be an integer.
4. Non-Perfect Cubes: If the number is not a perfect cube, the cubed root will be an irrational number (a non-repeating, non-terminating decimal), and calculators provide an approximation.
5. Calculator Precision: The number of decimal places your calculator (or this tool) displays affects the precision of the result shown, though the internal calculation is usually more precise.
6. Input Method on Calculator: When using a physical calculator with `x^y`, using `(1/3)` in parentheses is more accurate than `0.33333` if you don’t use enough decimal places for the latter.

Frequently Asked Questions (FAQ)

What is the cubed root of 1?

The cubed root of 1 is 1 (1 × 1 × 1 = 1).

What is the cubed root of -1?

The cubed root of -1 is -1 ((-1) × (-1) × (-1) = -1).

Can you find the cubed root of a negative number?

Yes, you can find the cubed root of any real number, including negative numbers. The result will be negative.

How do I find the cubed root without a calculator?

For perfect cubes, you might recognize them. For others, you can use estimation or numerical methods like the Newton-Raphson method, but these are more complex than using a calculator for finding the cubed root.

Is cubed root the same as raising to the power 1/3?

Yes, finding the cubed root of a number ‘x’ is exactly the same as calculating x^1/3.

How is the cubed root different from the square root?

The square root of ‘x’ is a number ‘y’ such that y × y = x (you can’t take the square root of a negative number in real numbers). The cubed root of ‘x’ is ‘y’ such that y × y × y = x (you can take the cubed root of any real number).

What button is cubed root on a calculator?

Look for ∛x, x^1/3, x^1/y, or use the x^y button with (1/3) as the exponent. Check your calculator’s manual for specifics on how to find the cubed root.

Where is the cubed root used?

It’s used in geometry (volumes), physics (some relationships), engineering, and any mathematical problem involving x³ where you need to solve for x.