CUBE ROOT OF THE GIVEN NUMBER
Cube root of a number is the factor that we multiply by itself three times to get that number. The symbol
To find a cube root of a number, we will follow the steps.
Step 1 :
Decompose the numerators and denominator separately as product of prime factors.
Step 2 :
For every three same value, we can take one out of the radical.
Finding cube root of rational number ?
Using the following property, we find cube root of rational number.
Cube root of negative numbers :
Cube root of negative number is also negative.
For example,
Evaluate each of the following:
Problem 1 :
∛-27
Solution :
= ∛-27
We can write 27 as 3 × 3 × 3,
∛-27 = ∛ - (3 × 3 × 3)
∛-27 = -3
Problem 2 :
∛1/8
Solution :
= ∛1/8
= ∛1/ ∛8
= 1/2
Problem 3 :
∛27
Solution :
= ∛27
We can write 27 as 3 × 3 × 3,
∛27 = ∛ (3 × 3 × 3)
∛27 = 3
Problem 4 :
- ∛1/64
Solution :
= -∛1/64
= -∛1/ ∛64
= -1/4
Problem 5 :
∛-8/27
Solution :
= ∛-8/27
= ∛-8/ ∛27
= -2/3
Problem 6 :
∛-1000
Solution :
= ∛-1000
We can write 1000 as 10 × 10 × 10,
∛-1000 = -∛ (10 × 10 × 10)
∛-1000 = -10
Problem 7 :
∛-27/64
Solution :
= ∛-27/64
= ∛-27/ ∛64
= -3/4
Problem 8:
-∛-64
Solution :
= -∛-64
We can write 64 as 4 × 4 × 4,
-∛-64 = -∛ -(4 × 4 × 4)
-∛-64 = 4
Problem 9 :
∛-1/125
Solution :
= ∛-1/125
= ∛-1/ ∛125
= -1/5
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