Cube roots of perfect cubes

Key Notes :

📚 Cube Roots of Perfect Cubes

What is a Cube Root?

The cube root of a number is a value that, when multiplied by itself three times, gives the original number.

Mathematically:

If a³=b, then ∛b=a

Example: ∛27=3 because 3×3×3=27

Perfect Cubes

A perfect cube is a number that is the cube of an integer.

Examples of perfect cubes:

• 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

✅ Quick Tip: The cube of n is n³.

Finding Cube Roots of Perfect Cubes

1. Identify the perfect cube.

2. Determine the number which, when cubed, gives that perfect cube.

Examples:

∛64=4 because 4³=64

∛125=5 because 5³=125

Properties of Cube Roots

• Every positive number has one positive cube root.
• Every negative number has one negative cube root.
• Cube roots of perfect cubes are always integers.

Example:

∛−27=−3 because (−3)³=−27

Shortcut/Trick to Remember Cube Roots

Unit digit method: The last digit of a perfect cube tells the last digit of its cube root:

Cube	Last Digit of Cube Root
1	1
8	2
27	3
64	4
125	5
216	6
343	7
512	8
729	9
1000	0

Quick Practice

1. Find: ∛512​ ✅ Answer: 8
2. Find: ∛−343​ ✅ Answer: -7
3. Find: ∛1000​ ✅ Answer: 10

💡 Remember: Cube roots undo cubing. If n³=x, then ∛x=n.

Learn with an example

Let’s practice!