Cube root of a number is the factor that we multiply by itself three times to get that number. The symbol
Find cube root of rational number ?
To find a cube root of a number, we will follow the steps.
Step 1 :
Decompose the numerator and denominator separately as product of prime factors.
Step 2 :
For every three same values, we can take one out of the radical.
Evaluate:
Problem 1 :
∛(1/125)
Solution :
∛(1/125)
Distribute the cube root to numerator and denominator.
= ∛1 / ∛125
Decompose the number inside the radical sign into prime factors.
= ∛(1 ∙ 1 ∙ 1) /∛(5 ∙ 5 ∙ 5)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 1/5
Problem 2 :
∛(-8/27)
Solution :
∛(-8/27)
Distribute the cube root to numerator and denominator.
= ∛-8 / ∛27
Decompose the number inside the radical sign into prime factors.
= - ∛(2 ∙ 2 ∙ 2) / ∛(3 ∙ 3 ∙ 3)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= -2/3
Problem 3 :
∛343/64
Solution :
∛(343/64)
Distribute the cube root to numerator and denominator.
= ∛(343 / 64)
Decompose the number inside the radical sign into prime factors.
= ∛(7 ∙ 7 ∙ 7) / ∛(4 ∙ 4 ∙ 4)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 7/4
Problem 4 :
-∛1 91/125
Solution :
= -∛1 91/125
= -∛(216/125)
Distribute the cube root to numerator and denominator.
= -∛(216 / 125)
Decompose the number inside the radical sign into prime factors.
= -∛(6 ∙ 6 ∙ 6) / ∛(5 ∙ 5 ∙ 5)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= -6/5
Problem 5 :
∛(1/64)
Solution :
∛(1/64)
Distribute the cube root to numerator and denominator.
= ∛(1 / 64)
Decompose the number inside the radical sign into prime factors.
= ∛(1 ∙ 1 ∙ 1) / ∛(4 ∙ 4 ∙ 4)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 1/4
Problem 6 :
∛3 3/8
Solution :
= ∛3 3/8
Converting the mixed fraction into improper fraction, we get
= ∛27/8
Distribute the cube root to numerator and denominator.
= ∛27 / 8
Decompose the number inside the radical sign into prime factors.
= ∛(3 ∙ 3 ∙ 3) / ∛(2 ∙ 2 ∙ 2)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 3/2
Problem 7 :
∛-216
Solution :
∛-216
We can write 216 as 6 × 6 × 6,
∛-216 = ∛(- 6 × -6 × -6)
∛-216 = -6
Problem 8 :
∛27/125
Solution :
∛(27/125)
Distribute the cube root to numerator and denominator.
= ∛(27 / 125)
Decompose the number inside the radical sign into prime factors.
= ∛(3 ∙ 3 ∙ 3) / ∛(5 ∙ 5 ∙ 5)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 3/5
Problem 9 :
- ∛(343/1000)
Solution :
- ∛(343/1000)
Distribute the cube root to numerator and denominator.
= -∛(343 / 1000)
Decompose the number inside the radical sign into prime factors.
= - ∛(7 ∙ 7 ∙ 7) / ∛(10 ∙ 10 ∙ 10)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= -7/10
Problem 10 :
∛729/64
Solution :
∛(729/64)
Distribute the cube root to numerator and denominator.
∛(729 / 64)
Decompose the number inside the radical sign into prime factors.
= ∛(9 ∙ 9 ∙ 9) / ∛(4 ∙ 4 ∙ 4)
Since the index is 3, we have to take one number out of radical sign for every three same numbers multiplied inside the radical sign.
= 9/4
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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