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Simplify Radical Expressions using the Distributive Property>
Simplify Radical Expressions using the Distributive Property 2Simplify Radical Expressions using the Distributive Property 2
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Question 1 of 5
1. Question
Simplify
`sqrt3 (sqrt5 + sqrt7)`
Hint
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Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)`Apply the Distributive Property.`color(darkviolet)(sqrt3)(color(royalblue)(sqrt5) + color(forestgreen)(sqrt7))` `=` `color(darkviolet)(sqrt3) xx color(royalblue)(sqrt5) + color(darkviolet)(sqrt3) xx color(forestgreen)(sqrt7)` `=` `sqrt(15) + sqrt(21)` Apply the Multiplication Property `sqrt(15)+sqrt(21)` -
Question 2 of 5
2. Question
Simplify
`sqrt5 (sqrt2 +8)`
Correct
Excellent!
Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)`Apply the Distributive Property.`color(darkviolet)(sqrt5)(color(royalblue)(sqrt2) + color(forestgreen)(8))` `=` `color(darkviolet)(sqrt5) xx color(royalblue)(sqrt2) + color(darkviolet)(sqrt5) xx color(forestgreen)(8)` `=` `sqrt(10) + 8sqrt(5)` Apply the Multiplication Property `sqrt(10)+8sqrt(5)` -
Question 3 of 5
3. Question
Simplify
`sqrt2 (sqrt2 – 4)`
Hint
Help VideoCorrect
Excellent!
Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)`Apply the Distributive Property.`color(darkviolet)(sqrt2)(color(royalblue)(sqrt2) – color(forestgreen)(4))` `=` `color(darkviolet)(sqrt2) xx color(royalblue)(sqrt(2)) – color(darkviolet)(sqrt2) xx color(forestgreen)(4)` `=` `2 – 4sqrt(2)` Apply the Multiplication Property `2 – 4sqrt(2)` -
Question 4 of 5
4. Question
Simplify
`3sqrt2 (4sqrt5 + 7)`
Hint
Help VideoCorrect
Excellent!
Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)`Apply the Distributive Property.`color(darkviolet)(3sqrt2)(color(royalblue)(4sqrt5) + color(forestgreen)(7))` `=` `color(darkviolet)(3sqrt2) xx color(royalblue)(4sqrt5) + color(darkviolet)(3sqrt2) xx color(forestgreen)(7)` `=` `12sqrt10 + 21sqrt2` Apply the Multiplication Property `12sqrt10 + 21sqrt2` -
Question 5 of 5
5. Question
Simplify
`3sqrt5 (sqrt5 – 2)`
Hint
Help VideoCorrect
Excellent!
Incorrect
Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)`Apply the Distributive Property.`color(darkviolet)(3sqrt5)(color(royalblue)(sqrt5) -color(forestgreen)(2))` `=` `color(darkviolet)(3sqrt5) xx color(royalblue)(sqrt5) – color(darkviolet)(3sqrt5) xx color(forestgreen)(2)` `=` `3sqrt25 – 6sqrt5` Apply the Multiplication Property `=` `3times5 – 6sqrt5` 25 is a Perfect Square `=` `15 – 6sqrt(5)` Simplify `15 – 6sqrt(5)`
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