Cube Root of 5 — Value and Steps

Q: What is the cube root of 5?

The cube root of 5 is $\sqrt[3]{5} \approx 1.710$, an irrational number.

Q: Can the cube root of 5 be simplified?

No. Because 5 is prime, it has no perfect-cube factor, so $\sqrt[3]{5}$ is already in simplest radical form.

Q: Is the cube root of 5 rational or irrational?

Irrational. Since 5 is not a perfect cube, $\sqrt[3]{5}$ is a non-terminating, non-repeating decimal.

Q: What is the cube root of 5 in exponential form?

It is $5^{1/3}$, which is the same as $\sqrt[3]{5}$.

Q: How is $\sqrt[3]{5}$ different from $\sqrt[3]{3}$?

Both are prime and irrational, but $\sqrt[3]{5} \approx 1.710$ is larger than $\sqrt[3]{3} \approx 1.442$, since 5 is a larger number under the same index.

The cube root of 5 is $\sqrt[3]{5} \approx 1.710$ , and because 5 is prime, the radical does not simplify.

Quick Answer:
Result: $\sqrt[3]{5} \approx 1.710$
Notation: $\sqrt[3]{5}$ or $5^{1/3}$
Method shown: estimation between neighbouring cubes
Approximate value: $1.710$ (to 3 decimal places, irrational)
Exact form: $\sqrt[3]{5}$ (already in simplest radical form)

Quick Reference Table

Number	Simplified cube root	Decimal (3 dp)
$\sqrt[3]{1}$	$1$	$1.000$
$\sqrt[3]{3}$	$\sqrt[3]{3}$	$1.442$
$\sqrt[3]{4}$	$\sqrt[3]{4}$	$1.587$
$\sqrt[3]{5}$	$\sqrt[3]{5}$	$1.710$
$\sqrt[3]{6}$	$\sqrt[3]{6}$	$1.817$
$\sqrt[3]{8}$	$2$	$2.000$

Where the Cube Root of 5 Appears

The cube root of 5 is the edge length of a cube whose volume is 5 cubic units. It also appears in scaling problems: a cube-shaped container whose capacity must grow five times, while staying a cube, needs each edge multiplied by $\sqrt[3]{5} \approx 1.710$ , not by 5.

What Is the Cube Root of 5?

The cube root of a number is the value that, multiplied by itself three times, returns that number. Since no whole number cubed equals 5, the cube root of 5 sits between $1^3 = 1$ and $2^3 = 8$ .

The result is an irrational number that never terminates and never repeats. Because 5 is prime, it carries no perfect-cube factor, so $\sqrt[3]{5}$ is already in its simplest form, the same principle at work across cube numbers and radicals.

How to Find the Cube Root of 5 (Methods)

Method 1: Estimation between neighbouring cubes

Locate 5 between the two nearest perfect cubes.

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

So $\sqrt[3]{5}$ lies between 1 and 2. Since 5 is roughly midway, start near the middle. Testing $1.7$ :

$1.7^3 = 4.913$

That is below 5, so try $1.72$ :

$1.72^3 \approx 5.088$

That is just above 5, so the answer sits between 1.70 and 1.72. Testing $1.710$ :

$1.710^3 \approx 5.000$

Final answer: $\sqrt[3]{5} \approx 1.710$ to three decimal places.

Method 2: Why it will not simplify

Write 5 in terms of its prime factors.

$5 = 5$

For a factor to leave a cube root, it must appear three times. The single 5 has no group of three.

$\sqrt[3]{5} = \sqrt[3]{5}$

Final answer: $\sqrt[3]{5}$ is already in simplest radical form.

Common Mistakes With Cube Root of 5

Mistake 1: Dropping the cube-root index

Where it slips in: writing the radical quickly.

Don't do this: writing $\sqrt{5}$ when you mean the cube root.

The correct way: always show the index: $\sqrt[3]{5}$ . Without the little 3 it reads as a square root, giving $\approx 2.236$ instead of $\approx 1.710$ .

Mistake 2: Trying to simplify a prime radical

Where it slips in: assuming every cube root breaks down like $\sqrt[3]{40} = 2\sqrt[3]{5}$ .

Don't do this: writing $\sqrt[3]{5}$ as a product of smaller radicals.

The correct way: a prime number under a cube root has no perfect-cube factor, so it stays as $\sqrt[3]{5}$ .

Mistake 3: Guessing the value is close to 2

Where it slips in: noticing 5 is near 8 and assuming the cube root is near 2.

Don't do this: answering roughly 1.9 or 2.

The correct way: cube roots grow slowly. Since $1.7^3 = 4.913$ , the answer is close to 1.71, not 2.

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 5?

The cube root of 5 is

\sqrt[3]{5} \approx 1.710

, an irrational number.

Can the cube root of 5 be simplified?

No. Because 5 is prime, it has no perfect-cube factor, so

\sqrt[3]{5}

is already in simplest radical form.

Is the cube root of 5 rational or irrational?

Irrational. Since 5 is not a perfect cube,

\sqrt[3]{5}

is a non-terminating, non-repeating decimal.

What is the cube root of 5 in exponential form?

It is

5^{1/3}

, which is the same as

\sqrt[3]{5}

How is

\sqrt[3]{5}

different from

\sqrt[3]{3}

Both are prime and irrational, but

\sqrt[3]{5} \approx 1.710

is larger than

\sqrt[3]{3} \approx 1.442

, since 5 is a larger number under the same index.

✍️ 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.