Square and cube roots of rational numbers worksheet :
Here we are going to see some practice questions on finding square and cube roots of rational numbers.
(1) Find the root of the following rational number
√64
(2) Find the root of the following rational number
√(1/4)
(3) Find the root of the following rational number
∛(8/125)
(4) Find the root of the following rational number
∛(1/64)
(5) Find the root of the following rational number
√(36/81)
(6) Find the root of the following rational number
√(81/100)
(7) Find the root of the following rational number
∛(125/216)
(8) Find the root of the following rational number
∛(125/27)
Question 1 : Find the root of the following rational number √64 Solution : Step 1 : Index of the given rational number is 2. = √64 Step 2 : Spliting the number as much as possible. = √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2) Step 3 : Since the index is 2, we have to take one common number for every two same terms. = 2 ⋅ 2 ⋅ 2 = 8 

Question 2 :
Find the root of the following rational number
√(1/4)
Solution :
Step 1 :
Index of the given rational number is 2.
= √(1/4)
Step 2 :
Spliting the number as much as possible.
= √(1/2) ⋅ (1/2)
Step 3 :
Since the index is 2, we have to take one common number for every two same terms.
= 1/2
Let us look into the solution of next problem on "Square and cube roots of rational numbers worksheet".
Question 3 :
Find the root of the following rational number
∛(8/125)
Solution :
Step 1 :
Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.
= ∛8/∛125
Step 2 :
Spliting the number as much as possible.
= ∛(2 ⋅ 2 ⋅ 2)/∛(5 ⋅ 5 ⋅ 5)
Step 3 :
Since the index is 3, we have to take one common number for every three same terms.
= 2/5
Question 4 :
Find the root of the following rational number
∛(1/64)
Solution :
Step 1 :
Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.
= ∛1/∛64
Step 2 :
Spliting the number as much as possible.
= ∛(1 ⋅ 1 ⋅ 1)/∛(4 ⋅ 4 ⋅ 4)
Step 3 :
Since the index is 3, we have to take one common number for every three same terms.
= 1/4
Question 5 :
Find the root of the following rational number
√(36/81)
Solution :
Step 1 :
Index of the given rational number is 2.Now we need to take separate square roots for both numerator and denominator.
= √(36/81)
= √36/√81
Step 2 :
Spliting the number as much as possible.
= √(2⋅2⋅3⋅3)/√(3⋅3⋅3⋅3)
Step 3 :
Since the index is 2, we have to take one common number for every two same terms.
= (2⋅3)/(3⋅3)
= 2/3
Question 6 :
Find the root of the following rational number
√(81/100)
Solution :
Step 1 :
Index of the given rational number is 2.Now we need to take separate square roots for both numerator and denominator.
= √(81/100)
= √81/√100
Step 2 :
Spliting the number as much as possible.
= √(3⋅3⋅3⋅3)/√(10⋅10)
Step 3 :
Since the index is 2, we have to take one common number for every two same terms.
= (2⋅3)/(3⋅3)
= 2/3
Question 7 :
Find the root of the following rational number
∛(125/216)
Solution :
Step 1 :
Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.
= ∛125/∛216
Step 2 :
Spliting the number as much as possible.
= ∛(5 ⋅ 5 ⋅ 5)/∛(6 ⋅ 6 ⋅ 6)
Step 3 :
Since the index is 3, we have to take one common number for every three same terms.
= 5/6
Question 8 :
Find the root of the following rational number
∛(125/27)
Solution :
Step 1 :
Index of the given rational number is 3.Now we need to take separate cube roots for both numerator and denominator.
= ∛125/∛27
Step 2 :
Spliting the number as much as possible.
= ∛(5 ⋅ 5 ⋅ 5)/∛(3 ⋅ 3 ⋅ 3)
Step 3 :
Since the index is 3, we have to take one common number for every three same terms.
= 5/3
After having gone through the stuff given above, we hope that the students would have understood "Square and cube roots of rational numbers worksheet"
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