DIVIDING RADICAL EXPRESSIONS WORKSHEET

Simplify the following radical expressions :

Question 1 :

√15/(5√10)

Question 2 :

√8/√100

Question 3 :

√6/√27

Question 4 :

√(3x²y³)/4√(5xy³)

Question 5 :

3/(4 + √5)

Question 6 :

5/(5 + 3√3)

Question 7 :

³√16/³√54

Question 8 :

³√64/√16

Question 9 :

³√16x⁹/³√2x⁶

Question 10 :

³√81x³y⁶/³√3x⁶y³

1. Answer :

= √15/(5√10)

  = (1/5)(√15/√10)

  =  (1/5)√(15/10)

  =  (1/5)√(3/2)

  =  √3/(5√2)

2. Answer :

= √8/√100

  = √(2 ⋅ 2 ⋅ 2)/√(5 ⋅ 5 ⋅ 2 ⋅ 2)

= 2√2/(5 ⋅ 2)

= 2√2/10

 =  √2/5

3. Answer :

 = √6/√27

= √(6/27)

= √2/√9

= √2/√(3 ⋅ 3 ⋅ 3)

  =  √2/3√3

4. Answer :

= √(3x²y³)/4√(5xy³)

= (1/4)√(3x²y³/5xy³)

= (1/4)√(3x/5)

= (1/4) √3x/√5

5. Answer :

= 3/(4 + √5)

In order to simplify the given radical expression, we need to multiply both numerator and denominator by the conjugate of 4 + √5.

Conjugate of 4 + √5 is 4 - √5.

= [3/(4 + √5)] x [(4 - √5) / (4 - √5)]

= [3(4 - √5)/(4 + √5) (4 - √5)]

= [3(4 - √5)/(4² - √5²)]

 = [3(4 - √5)/(16 - 5)]

= (12 - 3√5)/11

= (12/11) - (3√5/11)

6. Answer :

= 5/(5 + 3√3)

In order to simplify the given radical expression, we need to multiply both numerator and denominator by the conjugate of 5 + 3√3.

Conjugate of 5 + 3√3 is 5 - 3√3.

= [5/(5 + 3√3)] x [(5 - 3√3) / (5 - 3√3)]

= [5(5 - 3√3)/(5 + 3√3) (5 - 3√3)]

= [5(5 - 3√3)/(5² - (3√3)²)]

= [5(5 - 3√3)/(25 - (9(3))]

 = [5(5 - 3√3)/(25 - 27)]

= [5(5 - 3√3)/(-2)]

= [(25 - 15√3)/(-2)]

= 15√3 - 25/2

7. Answer :

= ³√16/³√54

= ³√(16/54)

= ³√(8/27)

= ³√8/³√27

  = ³√(2 ⋅ 2 ⋅ 2)/³√(3 ⋅ 3 ⋅ 3)

= 2/3

8. Answer :

= ³√64/√16

  = ³√(4³)/√(4²)

= 4/4

= 1

9. Answer :

= ³√(16x⁹/2x⁶)

 = ³√8x^9-6

= ³√(2³x³)

= 2x

10. Answer :

= ³√81x³y⁶/³√3x⁶y³

= ³√(81x³y⁶/3x⁶y³)

= ³√(27x^3-6y^6-3)

= ³√(27x^3-6y^6-3)

= ³√(27x^-3y³)

= ³√(3³y³/x³)

= ³√(3y/x)³

= 3y/x

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