# Cube Root of 24 — Value and Simplification Steps

TL;DR

The cube root of 24 simplifies to \(2\sqrt[3]{3}\), with a decimal value of about 2.884. This article shows the prime-factorization simplification, the estimation method, where it appears, common mistakes, and worked examples.

## Quick Reference Table

| Number             | Simplified cube root          | Decimal (3 dp) |
|--------------------|-------------------------------|-----------------|
| \(8\sqrt[3]{8}\) | \(2^2\)                     | 2.000           |
| \(16\sqrt[3]{16}\) | \(2^2\sqrt[3]{2}\)        | 2.520           |
| \(24\sqrt[3]{24}\) | \(2^3\sqrt[3]{3}\)        | 2.884           |
| \(27\sqrt[3]{27}\) | \(3\)                       | 3.000           |
| \(54\sqrt[3]{54}\) | \(3^2\sqrt[3]{2}\)        | 3.780           |
| \(64\sqrt[3]{64}\) | \(4\)                       | 4.000           |

## Where the Cube Root of 24 Appears

The cube root of 24 turns up whenever a volume is known and an edge length is wanted. If a cube-shaped tank holds 24 cubic units, each edge measures about \(2.884\) units. The same simplification pattern — pulling a perfect-cube factor out from under the radical — is what scientific and engineering calculators do internally before rounding.

## What Is the Cube Root of 24?

The cube root of a number is the value that, multiplied by itself three times, returns that number. Since 24 is not a perfect cube — it sits between \(8\) and \(27\) — its cube root is an irrational number that never terminates.

But it is not fully "stuck" under the radical. Because 24 contains the perfect-cube factor 8, part of it can come out, leaving the simplified form \(2\sqrt[3]{3}\). This is the same skill used across [cube numbers](/content/math/algebra/cube-numbers/index.html) and radicals.

## How to Simplify the Cube Root of 24 (Methods)

### **Method 1: Prime factorization**

Break 24 into its prime factors.

\[24=2 	imes 2 	imes 2 	imes 3 = 2^3 	imes 3\]

Write the cube root over the factored form.

\[\sqrt[3]{24} = \sqrt[3]{2^3 \times 3}\]

The cube root of \(2^3\) is 2, so 2 comes out of the radical while the 3 stays inside.

\[\sqrt[3]{24} = 2\sqrt[3]{3}\]

**Final answer:** \(\sqrt[3]{24} = 2\sqrt[3]{3}\).

### **Method 2: Estimation for the decimal value**

Locate 24 between neighbouring perfect cubes.

\[\sqrt[3]{24} \text{ lies between } 2 \text{ and } 3, \text{ and close to } 3 \text{ because } 24 \text{ is close to } 27.\]

Testing 2.9:

\[2.9^3 = 24.389\]

That is slightly above 24, so the answer is a touch below 2.9. Testing 2.88:

\[2.88^3 \approx 23.888\]

**Final answer:** \(\sqrt[3]{24} \approx 2.884\) to three decimal places.

## Common Mistakes With Cube Root of 24

### **Mistake 1: Dropping the cube-root index**

**Where it slips in:** writing the radical quickly.

**Don't do this:** writing \(\sqrt{24}\) when you mean the cube root.

**The correct way:** always show the index: \(\sqrt[3]{24}\). Without the little 3 it reads as a square root, giving approximately 4.899 instead of approximately 2.884.

### **Mistake 2: Pulling out the wrong factor**

**Where it slips in:** simplifying by removing any factor instead of a perfect-cube factor.

**Don't do this:** writing \(4\sqrt[3]{6}\) by splitting off 4.

**The correct way:** only a perfect _cube_ factor can leave the radical. Here that is 8, giving \(2\sqrt[3]{3}\).

### **Mistake 3: Treating the cube root like a square root when simplifying**

**Where it slips in:** grouping factors in pairs instead of triples.

**Don't do this:** taking one factor out for every pair of 2's.

**The correct way:** a cube root removes a factor for every _three_ copies. Three 2's give one 2 outside; the leftover 3 has no triple, so it stays inside.

## Frequently Asked Questions

What is the cube root of 24 in simplest radical form?

It is \(2\sqrt[3]{3}\), found by pulling the perfect-cube factor \(8\) out of 24.

Is the cube root of 24 rational or irrational?

Irrational. Since 24 is not a perfect cube, \(\sqrt[3]{24}\) is a non-terminating, non-repeating decimal, about 2.884.

What is the cube root of 24 as a decimal?

Approximately 2.884 to three decimal places.

Why does 2 come out of \(\sqrt[3]{24}\) but 3 does not?

Because \(24=2^3 \times 3\). The factor \(2^3\) is a perfect cube, so its cube root is the whole number 2; the lone 3 has no cube factor, so it remains under the radical.

How is the cube root of 24 different from the cube root of 27?

\(\sqrt[3]{27} = 3\) exactly, because 27 is a perfect cube. \(\sqrt[3]{24}\) is irrational and simplifies only to \(2\sqrt[3]{3}\.