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Simplify Radical Expressions using the Distributive Property>
Simplify Radical Expressions using the Distributive Property 1Simplify Radical Expressions using the Distributive Property 1
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Question 1 of 4
1. Question
Simplify`5 (sqrt2- 3)`Hint
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Single Bracket Expansion Method (Distributive Property)
`a``(``b``+``c``)=``a``b``+``a``c`Apply the Distributive Property.`5 (sqrt2- 3)` `=` `5 xx sqrt2 + 5 xx ( -3)` `=` `5sqrt(2)- 15` Simplify `5sqrt(2)- 15` -
Question 2 of 4
2. Question
Simplify`sqrt5 (sqrt7 -3)`Hint
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Single Bracket Expansion Method
(Distributive Property)`a``(``b``+``c``)=``a``b``+``a``c`Apply the Distributive Property.`sqrt5 (sqrt7 -3)` `=` `sqrt5 xx sqrt7 + sqrt5 xx (-3)` `=` `sqrt(35)- 3sqrt(5)` Apply the Multiplication Property `sqrt(35)- 3sqrt(5)` -
Question 3 of 4
3. Question
Simplify`2sqrt3 (4sqrt5- 2)`Hint
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Correct!
Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Single Bracket Expansion Method
(Distributive Property)`a``(``b``+``c``)=``a``b``+``a``c`Apply the Distributive Property.`2sqrt3 (4sqrt5- 2)` `=` `2sqrt3 xx 4sqrt5 + 2sqrt3 xx (-2)` `=` `2 xx 4 xx sqrt3 xx sqrt5 + 2 xx (-2) xx sqrt3` `=` `8 xx sqrt3 xx sqrt5- 4 xx sqrt3` `=` `8sqrt(15)- 4sqrt(3)` Apply the Multiplication Property `8sqrt(15) -4sqrt(3)` -
Question 4 of 4
4. Question
Simplify`(5+sqrt3) (7- sqrt2)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Double Bracket Expansion (FOIL) Method
`(``a``+``b``)(``c``+``d``)=``a``c``+``a``d``+``b``c``+``b``d`Apply the FOIL method.`(5+sqrt3) (7- sqrt2)` `=` `(5 xx 7)- (5 xx sqrt2) + (sqrt3 xx 7)- (sqrt3 xx sqrt2)` `=` `35- 5sqrt2 + 7sqrt3- sqrt3 xx sqrt2` `=` `35-5sqrt(2) + 7sqrt(3)-sqrt6` Apply the Multiplication Property `35-5sqrt(2) + 7sqrt(3)-sqrt6`
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