Cube Root of 3 — Value, Steps, and Estimation

Q: What is the cube root of 3?

The cube root of 3 is $\sqrt[3]{3} \approx 1.442$, an irrational number.

Q: Can the cube root of 3 be simplified?

No. Because 3 is prime, it has no perfect-cube factor, so $\sqrt[3]{3}$ is already in simplest radical form.

Q: Is the cube root of 3 rational or irrational?

Irrational. Since 3 is not a perfect cube, $\sqrt[3]{3}$ is a non-terminating, non-repeating decimal.

Q: What is the cube root of 3 in exponential form?

It is $3^{1/3}$, which is the same as $\sqrt[3]{3}$.

Q: How is $\sqrt[3]{3}$ different from $\sqrt{3}$?

$\sqrt{3} \approx 1.732$ asks which number squared gives 3, while $\sqrt[3]{3} \approx 1.442$ asks which number cubed gives 3. The index changes the answer.

The cube root of 3 is $\sqrt[3]{3} \approx 1.442$ , and unlike many radicals, it does not simplify at all.

Quick Answer:
Result: $\sqrt[3]{3} \approx 1.442$
Notation: $\sqrt[3]{3}$ or $3^{1/3}$
Method shown: estimation between neighbouring cubes
Approximate value: $1.442$ (to 3 decimal places, irrational)
Exact form: $\sqrt[3]{3}$ (already in simplest radical form)

Quick Reference Table

Number	Simplified cube root	Decimal (3 dp)
$\sqrt[3]{1}$	$1$	$1.000$
$\sqrt[3]{2}$	$\sqrt[3]{2}$	$1.260$
$\sqrt[3]{3}$	$\sqrt[3]{3}$	$1.442$
$\sqrt[3]{4}$	$\sqrt[3]{4}$	$1.587$
$\sqrt[3]{5}$	$\sqrt[3]{5}$	$1.710$
$\sqrt[3]{8}$	$2$	$2.000$

Where the Cube Root of 3 Appears

The cube root of 3 is the edge length of a cube whose volume is 3 cubic units. It also turns up in engineering scaling laws: to triple the volume of a cube-shaped object while keeping its proportions, every edge must grow by a factor of $\sqrt[3]{3} \approx 1.442$ , not by 3.

What Is the Cube Root of 3?

The cube root of a number is the value that, multiplied by itself three times, gives that number. Since no whole number cubed equals 3, the cube root of 3 sits between $1^3 = 1$ and $2^3 = 8$ .

The result is an irrational number that never terminates and never repeats. Because 3 is prime, it has no perfect-cube factor to pull out, so $\sqrt[3]{3}$ is already in its simplest form, a point that connects directly to the ideas in cube numbers and radicals.

How to Find the Cube Root of 3 (Methods)

Method 1: Estimation between neighbouring cubes

Locate 3 between the two nearest perfect cubes.

$1^3 = 1$ $2^3 = 8$

So $\sqrt[3]{3}$ lies between 1 and 2, and much closer to 1 because 3 is close to 1. Testing $1.4$ :

$1.4^3 = 2.744$

That is below 3, so try $1.45$ :

$1.45^3 \approx 3.048$

That is just above 3, so the answer sits between 1.44 and 1.45. Testing $1.442$ :

$1.442^3 \approx 2.999$

Final answer: $\sqrt[3]{3} \approx 1.442$ to three decimal places.

Method 2: Why it will not simplify

Write 3 in terms of its prime factors.

$3 = 3$

For a factor to leave a cube root, it must appear three times. The single 3 has no group of three.

$\sqrt[3]{3} = \sqrt[3]{3}$

Final answer: $\sqrt[3]{3}$ is already in simplest radical form.

Common Mistakes With Cube Root of 3

Mistake 1: Dropping the cube-root index

Where it slips in: writing the radical quickly.

Don't do this: writing $\sqrt{3}$ when you mean the cube root.

The correct way: always show the index: $\sqrt[3]{3}$ . Without the little 3 it reads as a square root, giving $\approx 1.732$ instead of $\approx 1.442$ .

Mistake 2: Trying to simplify a prime radical

Where it slips in: assuming every cube root breaks down like $\sqrt[3]{24} = 2\sqrt[3]{3}$ .

Don't do this: writing $\sqrt[3]{3}$ as some product of smaller radicals.

The correct way: a prime number under a cube root has no perfect-cube factor, so it stays as $\sqrt[3]{3}$ .

Mistake 3: Confusing $\sqrt[3]{3}$ with $\dfrac{3}{3}$ or $3 \div 3$

Where it slips in: reading the radical as ordinary division.

Don't do this: answering 1.

The correct way: the cube root asks "what number cubed gives 3?" The answer is $\approx 1.442$ , not 1.

To build cube-root fluency with a teacher, explore Bhanzu's algebra tutor or math classes online.

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Frequently Asked Questions

What is the cube root of 3?

The cube root of 3 is

\sqrt[3]{3} \approx 1.442

, an irrational number.

Can the cube root of 3 be simplified?

No. Because 3 is prime, it has no perfect-cube factor, so

\sqrt[3]{3}

is already in simplest radical form.

Is the cube root of 3 rational or irrational?

Irrational. Since 3 is not a perfect cube,

\sqrt[3]{3}

is a non-terminating, non-repeating decimal.

What is the cube root of 3 in exponential form?

It is

3^{1/3}

, which is the same as

\sqrt[3]{3}

How is

\sqrt[3]{3}

different from

\sqrt{3}

\sqrt{3} \approx 1.732

asks which number squared gives 3, while

\sqrt[3]{3} \approx 1.442

asks which number cubed gives 3. The index changes the answer.

✍️ Written By

Bhanzu Team

Content Creator and Editor

Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.