Rationalizing the Denominator 3
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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 Radicals with Variables 1
- Simplify Radicals with Variables 2
- Simplify Radicals with Variables 3
- Rewriting Entire and Mixed Radicals 1
- Rewriting Entire and Mixed Radicals 2
- Add and Subtract Radical Expressions (Basic) 1
- Add and Subtract Radical Expressions (Basic) 2
- Add and Subtract Radical Expressions (Basic) 3
- Add and Subtract Radical Expressions 1
- Add and Subtract Radical Expressions 2
- Add and Subtract Radical Expressions 3
- Multiply Radical Expressions 1
- Multiply Radical Expressions 2
- Multiply Radical Expressions 3
- Multiply Radical Expressions 4
- Divide Radical Expressions 1
- Divide Radical Expressions 2
- Divide Radical Expressions 3
- Multiply and Divide Radical Expressions
- Simplify Radical Expressions using the Distributive Property 1
- Simplify Radical Expressions using the Distributive Property 2
- Simplify Radical Expressions using the Distributive Property 3
- Simplify Binomial Radical Expressions using the FOIL Method 1
- Simplify Binomial Radical Expressions using the FOIL Method 2
- Rationalizing the Denominator 1
- Rationalizing the Denominator 2
- Rationalizing the Denominator 3
- Rationalizing the Denominator 4
- Rationalizing the Denominator using Conjugates