CUBE ROOT
Definition Of Cube Root
Cube root of a number a is given as 
or 
. For example cube root of 64 =
=
=4.
More About Cube Root
Cube root is nothing but the one of the identical factors of a given number.
All the real numbers have exactly one real cube root and 2 complex roots.
All the non-zero complex numbers have three distinct cube roots.
Video Examples: Cube Root
Example of Cube Root
Cube root of 724 is 
= 9, because 9 × 9 × 9 = 724.
Cube root of x3y6z3 is 
.
Solved Example on Cube Root
Ques: Find the cube root of 1331.
Choices:
A. 11
B. 9
C. 12
D. 12.1
Correct Answer: A
Solution:
Step 1: Cube root of 1331 = 
Step 2: = 
[
= (a)1/n.]
Step 3: 
= [1331 can be written as 11 × 11 × 11 = 113.]
Step 4: = 113 . 1/3 [(an)m = amn]
Step 5: = 11
Step 6: So, cube root of 1331 is 11.
Quick Summary
- Cube root is one of the identical factors of a given number.
- Every real number has exactly one real cube root.
- Non-zero complex numbers have three distinct cube roots.
🍎 Teacher Insights
Use visual aids like cubes to demonstrate the concept of cube roots. Emphasize the difference between cube roots and square roots. Include examples with both positive and negative numbers.🎓 Prerequisites
- Exponents
- Multiplication
- Factors
Check Your Knowledge
Q1: What is the cube root of 8?
Q2: What is the cube root of -27?
Q3: Simplify ∛(x^6)
Frequently Asked Questions
Q: How do I find the cube root of a number?
A: You can find the cube root by finding a number that, when multiplied by itself three times, equals the original number. Prime factorization can help. Calculators also have a cube root function.
Q: Is the cube root of a negative number always negative?
A: Yes, the cube root of a negative real number is always a negative real number.
Q: How many cube roots does a complex number have?
A: A non-zero complex number has three distinct cube roots.