Cube Root Key on a Calculator: How to Use It

This page explains what a cube root key on a calculator does, how to use it correctly, and what to do if your calculator lacks one. You enter a number, press the cube root key (often labeled ∛ or accessed via a shift or second function), and the calculator returns the value that, when multiplied by itself three times, equals your original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.

Formula

The cube root of a number n is written as ∛n and is the inverse operation of cubing. The formula is:

∛n = x, where x³ = n

For a positive number, the cube root is positive; for a negative number, the cube root is negative. Unlike square roots, cube roots of negative numbers are real numbers. For instance, ∛(-8) = -2 because (-2)³ = -8.

Worked Example

Using the default value from the calculator above, n = 27:

1. Start with the equation x³ = 27.
2. Take the cube root of both sides: x = ∛27.
3. Recognize that 3 × 3 × 3 = 27, so x = 3.
4. The calculator displays 3 as the cube root.

The same result appears in the calculator block above, which rounds to 4 decimal places (3.0000).

Where to Find the Cube Root Key

Cube root keys vary by calculator model. On many scientific calculators, the cube root function is printed above the xʸ or ^ key and requires pressing a shift or 2nd function button first. On graphing calculators, it may be in a menu under math functions. On basic four-function calculators, there is usually no cube root key at all, but you can still compute it using the power function if available.

How to Use the Cube Root Key

• Enter the number you want the cube root of.
• Press the shift or 2nd button if the cube root symbol is printed above another key.
• Press the key with the ∛ symbol.
• Press equals or enter to see the result.

Some calculators work in the opposite order: press the cube root key first, then enter the number, then equals. Check your manual if unsure.

What If Your Calculator Doesn’t Have a Cube Root Key?

If your calculator lacks a dedicated cube root key, you can still calculate cube roots using the power function. The cube root of n equals n raised to the power of 1/3. So, on a calculator with a y^x or ^ key, enter n, press the power key, enter (1/3), and press equals. For example, to find ∛125, enter 125, press ^, enter (1/3), and get 5.

Another method is to use the general root function if your calculator has one (often labeled x√y). In that case, enter 3 as the root index, then the number.

Common Mistakes and Misconceptions

• Confusing cube root with square root: square root asks what number multiplied by itself once gives n; cube root asks for three multiplications.
• Forgetting that cube roots of negative numbers are negative: ∛(-64) = -4, not an error.
• Using the wrong order of operations on a calculator: if you press the cube root key before entering the number, some calculators may interpret it differently.
• Rounding too early in multi-step problems: keep full precision until the final answer.

When to Use Cube Roots

Cube roots appear in geometry when finding the side length of a cube from its volume, in physics for cubic scaling laws, and in statistics for calculating the cube root transformation of data. They also appear in formulas for the volume of spheres and in some financial calculations involving cubic growth.

Limitations of the Cube Root Key

The cube root key on a calculator gives a numerical approximation for most inputs, since many cube roots are irrational. For example, ∛2 is approximately 1.2599210498948732. The calculator’s display may round this, so for exact symbolic answers you would need a computer algebra system. Also, some calculators only accept non-negative inputs for cube roots, even though negative inputs are mathematically valid.

Frequently Asked Questions

How do I type cube root on a scientific calculator?

Look for a key labeled ∛, often printed above the xʸ key. Press shift or 2nd, then that key, then enter the number, then equals. If there is no ∛ key, use the power key with exponent 1/3.

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

Yes, mathematically they are identical. The cube root of n is n^(1/3). On calculators without a dedicated key, this is the standard alternative method.

Can I find cube root on a phone calculator?

Most phone calculator apps have a scientific mode. Rotate your phone to landscape or tap the scientific button to reveal the cube root function or the power key. If not, use the power key with 1/3 as the exponent.

Why does my calculator give an error for cube root of a negative number?

Some basic calculators only support square roots and reject negative inputs for any root function. Use a scientific calculator or the power method with parentheses: (-8)^(1/3) gives -2 on calculators that handle negative bases correctly.

What is the cube root of 0?

The cube root of 0 is 0, because 0 × 0 × 0 = 0. This is a valid result on any calculator.

How do I check if my cube root answer is correct?

Multiply the result by itself three times. If the product equals your original number, the answer is correct. For example, if you got 3 for ∛27, then 3 × 3 × 3 = 27, confirming the result.

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in n | Number | - | 27 | 0
out cube_root | Cube root | - | cbrt(n) | 4
out cube | Cube of input | - | n^3 | 0