Rationalizing the Denominator 4
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Question 1 of 6
1. Question
Rationalise the denominator:
`(sqrt6 + sqrt3)/(2sqrt6)`
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)``(sqrt6 + sqrt3)/(2sqrt6)` `=` `(sqrt6 + sqrt3)/(2sqrt6) xx color(crimson)((sqrt6)/(sqrt6))` `=` `((sqrt6 + sqrt3) xx sqrt6)/(2 xx (sqrt6 xx sqrt6))` `=` `(sqrt6 xx sqrt6+ sqrt3 xx sqrt6)/(2 xx (sqrt6 xx sqrt6)` Apply Distributive Property of Multiplication `=` `(sqrt36 + sqrt18)/(2 xx sqrt36)` Apply the Multiplication Property `=` `(6+3sqrt2)/12` `sqrt(36) = 6` and `sqrt(18) = 3sqrt2` `=` `(2+sqrt2)/4` Simplify `(2+sqrt2)/4` -
Question 2 of 6
2. Question
Rationalise the denominator:
`(sqrt10 – sqrt5)/(5sqrt10)`
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)``(sqrt10 – sqrt5)/(5sqrt10)` `=` `(sqrt10 – sqrt5)/(5sqrt10) xx color(crimson)((sqrt10)/(sqrt10))` `=` `((sqrt10 – sqrt5) xx sqrt10)/(5 xx (sqrt10 xx sqrt10))` `=` `(sqrt10 xx sqrt10- sqrt5 xx sqrt10)/(5 xx (sqrt10 xx sqrt10)` Apply Distributive Property of Multiplication `=` `(sqrt100 – sqrt50)/(5 xx sqrt100)` Apply the Multiplication Property `=` `(10 – 5sqrt2)/(50)` `sqrt(100) = 10` and `sqrt(50) = 5sqrt2` `=` `(2-sqrt2)/10` Simplify `(2-sqrt2)/10` -
Question 3 of 6
3. Question
Rationalise the denominator:`2/(3-sqrt2)`Hint
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Great Work!
Incorrect
For the answer to be in simplest form, the denominator should be a rational number.Since the denominator is a binomial, multiply the numerator and the denominator by `3+sqrt2`This is simply the denominator but with the opposite operation`2/(3-sqrt2)` `=` `2/(3-sqrt2) xx ``(3+sqrt2)/(3+sqrt2)` `=` `(2 xx (3+sqrt2))/((3-sqrt2) xx (3+sqrt2))` `=` `(6+2sqrt2)/(9-2)` Apply Multiplication Property `=` `(6+2sqrt2)/(9-2)` Apply Multiplication Property `=` `(6+2sqrt2)/7` `(6+2sqrt2)/7` -
Question 4 of 6
4. Question
Rationalise the denominator:`2/(sqrt3-1)`Hint
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Great Work!
Incorrect
For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt3+1``2/(sqrt3-1)` `=` `2/(sqrt3-1) xx ``(sqrt3+1)/(sqrt3+1)` `=` `(2 xx (sqrt3+1))/((sqrt3-1) xx (sqrt3+1))` `=` `(2sqrt3+2)/(sqrt9+sqrt3-sqrt3-1)` Expand the brackets `=` `(2sqrt3+2)/(3-1)` `sqrt(9) = 3` `=` `(2sqrt3+2)/2` `=` `sqrt3+1` `sqrt3+1` -
Question 5 of 6
5. Question
Rationalise the denominator:`(sqrt6+1)/(sqrt6+sqrt2)`Hint
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Excellent!
Incorrect
For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt6-sqrt2``(sqrt6+1)/(sqrt6+sqrt2)` `=` `(sqrt6+1)/(sqrt6+sqrt2) xx``(sqrt6-sqrt2)/(sqrt6-sqrt2)` `=` `((sqrt6+1)(sqrt6-sqrt2))/((sqrt6+sqrt2)(sqrt6-sqrt2))` `=` `(6-sqrt12+sqrt6-sqrt2)/(6-2)` Expand the brackets `=` `(6-2sqrt3+sqrt6-sqrt2)/4` `(6-2sqrt3+sqrt6-sqrt2)/4` -
Question 6 of 6
6. Question
Rationalise the denominator:`(sqrt5-sqrt2)/(sqrt5+sqrt2)`Hint
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Well Done!
Incorrect
For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt5-sqrt2``(sqrt5-sqrt2)/(sqrt5+sqrt2)` `=` `(sqrt5-sqrt2)/(sqrt5+sqrt2) xx``(sqrt5-sqrt2)/(sqrt5-sqrt2)` `=` `((sqrt5-sqrt2)(sqrt5-sqrt2))/((sqrt5+sqrt2)(sqrt5-sqrt2))` `=` `(5-sqrt10-sqrt10+2)/(5-2)` Expand the brackets `=` `(7-2sqrt10)/3` `(7-2sqrt10)/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