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Simplify Radical Expressions using the Distributive Property>
Simplify Radical Expressions using the Distributive Property 3Simplify Radical Expressions using the Distributive Property 3
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Question 1 of 5
1. Question
Simplify
`5sqrt6 (3sqrt6 – 3sqrt2)`
Hint
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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)(5sqrt6)(color(royalblue)(3sqrt6) -color(forestgreen)(3sqrt2))` `=` `color(darkviolet)(5sqrt6) xx color(royalblue)(3sqrt6) – color(darkviolet)(5sqrt6) xx color(forestgreen)(3sqrt2)` `=` `15sqrt(36) – 15sqrt(12)` Apply the Multiplication Property `=` `15 xx 6 – 15 xx 2sqrt(3)` Simplifying Surds `=` `90 – 30sqrt(3)` Simplify `90 – 30sqrt(3)` -
Question 2 of 5
2. Question
Simplify`(2sqrt3+3sqrt5) (2sqrt3 + 3sqrt5)`Hint
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Keep Going!
Incorrect
Multiplication Property of Radicals
`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.`(2sqrt3+3sqrt5) (2sqrt3 + 3sqrt5)` `=` `(2sqrt3 xx 2sqrt3) + (2sqrt3 xx 3sqrt5)` `+(3sqrt5 xx 2sqrt3) + (3sqrt5 xx 3sqrt5)` `=` `4sqrt9 + 6sqrt(15) + 6sqrt(15) + 9sqrt25` Apply the Multiplication Property `=` `4 xx 3 + 12sqrt(15) + 9 xx 5` Simplify `=` `12 + 12sqrt(15) + 45` `=` `57 + 12sqrt(15)` `57 + 12sqrt(15)` -
Question 3 of 5
3. Question
Simplify
`4sqrt5 (2sqrt5 – 4sqrt15)`
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)(4sqrt5)(color(royalblue)(2sqrt5) -color(forestgreen)(4sqrt15))` `=` `color(darkviolet)(4sqrt5) xx color(royalblue)(2sqrt5) – color(darkviolet)(4sqrt5) xx color(forestgreen)(4sqrt15)` `=` `8sqrt(25) – 16sqrt(75)` Apply the Multiplication Property `=` `8 xx 5 – 16 xx 5sqrt(3)` Simplifying Radicals `=` `40 – 80sqrt(3)` Simplify `40 – 80sqrt(3)` -
Question 4 of 5
4. Question
Simplify`(3sqrt11+4) (3sqrt11 -4)`Hint
Help VideoCorrect
Fantastic!
Incorrect
Multiplication Property of Radicals
`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.`(3sqrt11+4) (3sqrt11 -4)` `=` `(3sqrt11 xx 3sqrt11) + (3sqrt11 xx (-4))` `+(4 xx 3sqrt11) + (4 xx (-4))` `=` `9sqrt121- 12sqrt(11) + 12sqrt(11) -16` Apply the Multiplication Property `=` `9 xx 11 -16` Simplify `=` `99-16` `=` `83` `83` -
Question 5 of 5
5. Question
Simplify
`2sqrt(x) (3sqrt(x) + 2sqrt(y))`
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)(2sqrt(x))(color(royalblue)(3sqrt(x)) + color(forestgreen)(2sqrt(y)))` `=` `color(darkviolet)(2sqrt(x)) xx color(royalblue)(3sqrt(x)) + color(darkviolet)(2sqrt(x)) xx color(forestgreen)(2sqrt(y))` `=` `6sqrt(x^2) + 4sqrt(xy)` Apply the Multiplication Property `=` `6x + 4sqrt(xy)` Simplify `6x + 4sqrt(xy)`
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