# Cube Root of 5 — Value and Steps

TL;DR

The cube root of 5 is 53≈1.710, an irrational number that cannot be simplified because 5 is prime. This article shows why the radical stays as is, how to estimate its value by hand, where it appears, common mistakes, and worked examples.

The cube root of 5 is 53≈1.710, and because 5 is prime, the radical does not simplify.

> **Quick Answer:**  
> **Result:** 53≈1.710  
> **Notation:** 53 or 51/3  
> **Method shown:** estimation between neighbouring cubes  
> **Approximate value:** 1.710 (to 3 decimal places, irrational)  
> **Exact form:** 53 (already in simplest radical form)

## Quick Reference Table

| Number        | Simplified cube root | Decimal (3 dp) |  
|---------------|----------------------|----------------|
| 13            | 1                    | 1.000          |  
| 33            | 33                   | 1.442          |  
| 43            | 43                   | 1.587          |  
| 53            | 53                   | 1.710          |  
| 63            | 63                   | 1.817          |  
| 83            | 222                  | 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 53≈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 and 2.

The result is an irrational number that never terminates and never repeats. Because 5 is prime, it carries no perfect-cube factor, so 53 is already in its simplest form.

## How to Find the Cube Root of 5 (Methods)

### **Method 1: Estimation between neighbouring cubes**

Locate 5 between the two nearest perfect cubes.

So 53 lies between 1 and 2. Since 5 is roughly midway, start near the middle. Testing 1.7:

That is below 5, so try 1.72:

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

**Final answer:** 53≈1.710 to three decimal places.

### **Method 2: Why it will not simplify**

Write 5 in terms of its prime factors.

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

**Final answer:** 53 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.

**The correct way:** always show the index: 53. Without the little 3 it reads as a square root, giving ≈2.236 instead of ≈1.710.

### **Mistake 2: Trying to simplify a prime radical**

**Where it slips in:** assuming every cube root breaks down like 40.

**The correct way:** a prime number under a cube root has no perfect-cube factor, so it stays as 53.

### **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.

**The correct way:** cube roots grow slowly, the answer is close to 1.71, not 2.

## Frequently Asked Questions

**What is the cube root of 5?**

The cube root of 5 is 53≈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 53 is already in simplest radical form.

**Is the cube root of 5 rational or irrational?**

Irrational. Since 5 is not a perfect cube, 53 is a non-terminating, non-repeating decimal.

**What is the cube root of 5 in exponential form?**

It is 51/3, which is the same as 53.