 # Cube Root of 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.

The value of the cube root of 3, 3√3, is equal to 1.44224957031. 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. In this article, we will learn to find cube root by the approximation method.

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

## 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.

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

Then, x = 3√3

• 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.

• 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

• Again, divide this value by 1.4.

2.1428/1.4 = 1.53

• 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 25.

 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

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