Introduction
The cube root of a number is a value that, when multiplied by itself three times, gives us the original number. Hence, finding the cube root is the converse of finding the cube of a number.
The cube root of a number is denoted by the symbol ‘\( \sqrt[3]{~~} \)’ in radical form.
For example, the cube root of a number \( x \) is written as \( \sqrt[3]{x} \) .
In exponent form, the cube root of x is denoted by \( x^{\frac{1}{3}} \).
Cube Root 1 to 20
Cube root 1 to 20 (with values rounded up to four decimal places) is a table in which the cube root of numbers from 1 to 20 are listed.
These cube root values can be used to solve related math problems.
From the table we can observe that between 1 to 20 only 1 and 8 are perfect cube numbers. Hence the cube root of numbers, other than 1 and 8, are irrational numbers and their values will be non terminating non repeating. These cube roots are written up to four decimal places.
For ease of calculation, we mostly use the cube root value up to three decimal places.
Cube Root 1 to 20 (Rounded up to Three Decimal Places)
Solved Examples
Example 1: Find the value of \( \sqrt[3]{11} + \sqrt[3]{12} \).
Solution:
\( \sqrt[3]{11} + \sqrt[3]{12} \) [Write the given expression]
From the table substitute \( 2.224 \) for \( \sqrt[3]{11} \) and \( 2.289 \) for \( \sqrt[3]{12} \).
\( = 2.224 + 2.289 \)
\( = 4.513 \) [Add]
Therefore \( \sqrt[3]{11} + \sqrt[3]{12} \) is equal to \( 4.513 \).
Example 2: The volume of the cubical box given below is \( 18 \) cubic inches. Find the side length of the box.
Solution:
Let the side length of the box be \( x \) inches.
Volume of cube \( = x^3 \) [Volume of cube formula]
\( x^3 = 18 \) [Substitute \( 18 \) for volume]
\( \Rightarrow x = \sqrt[3]{18} \) [Cube root on both sides]
\( \Rightarrow x = 2.621 \)
So, the side length of the cubical box is \( 2.621 \) inches.
Example 3: Find the value of \( 2\sqrt[3]{14} + 3 \).
Solution:
\( 2\sqrt[3]{14} + 3 \) [Write the given expression]
From the table substitute \( 2.410 \) for \( \sqrt[3]{14} \).
\( = 2 \times 2.410 + 3 \)
\( = 4.82 + 3 \)
\( = 7.82 \)
So, \( 2\sqrt[3]{14} + 3 = 7.82 \).
Example 4: Find the value of \( \frac{\sqrt[3]{19}}{2} + \sqrt[3]{6} \).
Solution:
\( \frac{\sqrt[3]{19}}{2} + \sqrt[3]{6} \)
From the table substitute \( 2.668 \) for \( \sqrt[3]{19} \) and \( 1.817 \) for \( \sqrt[3]{6} \)
\( = \frac{2.668}{2} + 1.817 \)
\( = 1.334 + 1.817 \)
\( = 3.151 \)
So, \( \frac{\sqrt[3]{19}}{2} + \sqrt[3]{6} = 3.151 \).
The long division method can be used to calculate the cube root of numbers that are not perfect cube numbers.
There are three methods to find the cube root of a number:
- Prime factorization method
- Estimation method
- Long Division method
There are only two perfect cube numbers that are 1 and 8, between 1 to 20.
18 irrational cube roots appear in the list of cube roots from 1 to 20.
Cube root of 8 is 2, which is a rational number.