# Cube Root of 3

## Trigonometry # Cube Root of 3

The value of the cube root of 3 is equal to 1.44224957031. Cube root of 3 in radical form is represented as 3√3 and in exponential form as 31/3. Since 3 is not a perfect cube, therefore it is a little difficult to find its cube root. But, for perfect cubes like 8, 27, etc., the cube root of such numbers are whole numbers, because, 23 = 2×2×2 = 8 and 33 = 3×3×3 = 27. Hence, cube root of 8 is 2 and of 27 is 3.

Cube root of any number n is a number x, such as x3 = n. Hence, to find the cube root of 3 we have to determine a number, which when multiplied three times, gives the number 3, such as x3 = 3 or x = 3√3. Therefore, we need to find here the value of x.  In this article, we will learn to find cube root by the approximation method.

Cube Root Symbol: The symbol of cube root is ‘3√’

## What is Cube Root of 3?

The cube root of 3 is a value that results in the original number when multiplied by itself, three times. Since 3 is a prime number, thus, it has only two factors, 1 and 3. Hence, 3 cannot be factorised into a product of three whole numbers. So, the cube root of 3 is a fraction or decimal value. Also, the cube root of 3 is a rational number, since it cannot be expressed in the form of P/Q, where Q ≠ 0. It is represented by 3√3, in radical form.

3√3 = 1.4422 (up to four places of the decimal)

## How to find Cube root of 3?

Before we learn to find the cube root of number 3, we have to first learn the cubes of these numbers.

 Number (x) Cube of Number (x3) 1 1×1×1 = 1 2 2×2×2 = 8 3 3×3×3 = 27 4 4×4×4 = 64 5 5×5×5 = 125 6 6×6×6 = 216 7 7×7×7 = 343 8 8×8×8 = 512 9 9×9×9 = 729 10 10×10×10 = 1000

### Steps to find Cube Root Easily

Now, let us figure out the value of 3√3, step by step.

Step 1: Let us assume the cube root of 3 is equal to x.

Then, x = 3√3

Step 2: As we know,

13 = 1 and 23 = 8

Hence, x lies between 1 and 8. But, it lies closer to number 1 than 8, if we see in a number line. Hence, we can assume a value, say 1.4, which could be approx to the cube root of 3.

Step 3: Now to determine the value of 3√3, we need to divide 3 by the estimated value.

Divide 3 by 1.4.

3/1.4 = 2.1428

Step 4: Again, divide this value by 1.4.

2.1428/1.4 = 1.53

Step 5: Now, take the average of 1.4, 1.4 and 1.53 to get a value of 3√3.

(1.4+1.4+1.53)/3 = 1.44

The actual value of 3√3 is 1.442249.

Hence, 1.44 is approximately equal to 1.442249.

## Cube Root Lists

Below is the table for the cube root of numbers from 1 to 15.

 Number Cube root ∛a 1 1.000 2 1.260 3 1.442 4 1.587 5 1.710 6 1.817 7 1.913 8 2.000 9 2.080 10 2.154 11 2.224 12 2.289 13 2.351 14 2.410 15 2.466

## Solved Examples

Q.1: The volume of a cube is 24 cu.cm. What is the length of its edges?

Solution: Given,

volume of cube = 24 cu.cm

By the formula, we know,

volume of cube = a3, where a is the edge-length

24 = a3

a = 3√24 = 3√(2 x 2 x 2 x 3) = 23√3 = 2 x 1.442 = 2.884 cm

Hence, the length of edges of the cube is 2.884 cm.

Q.2: What is the value of 3√27 + 3√3 + 3√125? (Answer in radical form)

Solution: 3√27 + 3√3 + 3√125

3√(3 x 3 x 3) + 3√3 + 3√(5 x 5 x 5)

= 3 + 3√3 + 5

= 8 + 3√3

## Frequently Asked Questions – FAQs

### What is the value of cube root of 3?

The value of the cube root of 3 is 1.4422 up to four places of decimal.

### What is the value of cube root of 3 in radical form?

The value of cube root of 3 in radical form is 3√3.

### Is 3 a perfect cube?

3 is not a perfect cube since its cube root does result in a whole number.

### What is the cube of cube root of 3?

The cube of cube root of 3 is equal to 3.

Students can learn these values and solve questions based on them easily.