Rationalising the Denominator 3
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
Rationalise the denominator:
`6/(sqrt2)`
Correct
Excellent!
Incorrect
Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))`For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `color(crimson)(sqrt2)``6/(sqrt2)` `=` `6/(sqrt2) xx color(crimson)((sqrt2)/(sqrt2))` `=` `(6sqrt2)/(sqrt2 xx sqrt2)` `=` `(6sqrt2)/(sqrt4)` Apply the Multiplication Property `=` `(6sqrt2)/2` `sqrt(4) = 2` `=` `3sqrt2` Simplify `3sqrt2` -
Question 2 of 5
2. Question
Rationalise the denominator:
`(sqrt5)/(sqrt10)`
Correct
Excellent!
Incorrect
Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))`For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `color(crimson)(sqrt10)``(sqrt5)/(sqrt10)` `=` `(sqrt5)/(sqrt10) xx color(crimson)((sqrt10)/(sqrt10))` `=` `(sqrt50)/(sqrt10 xx sqrt10)` `=` `(sqrt50)/(sqrt100)` Apply the Multiplication Property `=` `(sqrt50)/10` `sqrt(100) = 10` `=` `(5sqrt2)/10` `sqrt50 = 5sqrt2` `=` `sqrt2/2` Simplify `sqrt2/2` -
Question 3 of 5
3. Question
Rationalise the denominator:
`3/(5sqrt3)`
Correct
Excellent!
Incorrect
Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))`For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `color(crimson)(sqrt3)``3/(5sqrt3)` `=` `3/(5sqrt3) xx color(crimson)((sqrt3)/(sqrt3))` `=` `(3sqrt3)/(5 xx(sqrt3 xx sqrt3))` `=` `(3sqrt3)/(5 xx sqrt9)` Apply the Multiplication Property `=` `(3sqrt3)/(5 xx 3)` `sqrt(9) = 3` `=` `(3sqrt3)/15` `5 xx 3 = 15` `=` `(sqrt3)/5` Simplify `(sqrt3)/5` -
Question 4 of 5
4. Question
Rationalise the denominator:
`(sqrt(5) + 1)/(sqrt6)`
Correct
Excellent!
Incorrect
Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))`For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `color(crimson)(sqrt6)``(sqrt(5) + 1)/(sqrt6)` `=` `(sqrt(5) + 1)/(sqrt6) xx color(crimson)((sqrt6)/(sqrt6))` `=` `((sqrt(5) + 1) xx sqrt6 )/(sqrt6 xx sqrt6)` Apply Distributive Property of Multiplication `=` `(sqrt(5) xx sqrt6 + 1 xx sqrt6 )/(sqrt6 xx sqrt6)` `=` `(sqrt30 + sqrt6)/(sqrt36)` Apply the Multiplication Property `=` `(sqrt30 + sqrt6)/6` `sqrt(36) = 6` `(sqrt30 + sqrt6)/6` -
Question 5 of 5
5. Question
Rationalise the denominator:
`(2sqrt6)/(3sqrt2)`
Correct
Excellent!
Incorrect
Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))`For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `color(crimson)(sqrt2)``(2sqrt6)/(3sqrt2)` `=` `(2sqrt6)/(3sqrt2) xx color(crimson)((sqrt2)/(sqrt2))` `=` `(2sqrt6 xx sqrt2)/(3 xx (sqrt2 xx sqrt2))` `=` `(2sqrt12)/(3sqrt4)` Apply the Multiplication Property `=` `(2sqrt12)/(3 xx 2)` `sqrt(4) = 2` `=` `(2 xx 2sqrt3)/6` `sqrt(12) = 2sqrt3` `=` `(2sqrt3)/3` Simplify `(2sqrt3)/3`
Quizzes
- Simplify Square Roots 1
- Simplify Square Roots 2
- Simplify Square Roots 3
- Simplify Square Roots 4
- Simplify Surds with Variables 1
- Simplify Surds with Variables 2
- Simplify Surds with Variables 3
- Rewriting Entire and Mixed Surds 1
- Rewriting Entire and Mixed Surds 2
- Add and Subtract Surd Expressions (Basic) 1
- Add and Subtract Surd Expressions (Basic) 2
- Add and Subtract Surd Expressions (Basic) 3
- Add and Subtract Surd Expressions 1
- Add and Subtract Surd Expressions 2
- Add and Subtract Surd Expressions 3
- Multiply Surd Expressions 1
- Multiply Surd Expressions 2
- Multiply Surd Expressions 3
- Multiply Surd Expressions 4
- Divide Surd Expressions 1
- Divide Surd Expressions 2
- Divide Surd Expressions 3
- Multiply and Divide Surd Expressions
- Simplify Surd Expressions using the Distributive Property 1
- Simplify Surd Expressions using the Distributive Property 2
- Simplify Surd Expressions using the Distributive Property 3
- Simplify Binomial Surd Expressions using the FOIL Method 1
- Simplify Binomial Surd Expressions using the FOIL Method 2
- Rationalising the Denominator 1
- Rationalising the Denominator 2
- Rationalising the Denominator 3
- Rationalising the Denominator 4
- Rationalising the Denominator using Conjugates