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Multiply and Divide Radical ExpressionsMultiply and Divide Radical Expressions
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Question 1 of 6
1. Question
Simplify
`(4sqrt8times2sqrt5)/(8sqrt20)`
Correct
Nice Work!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))` or `sqrt(a -: b)=sqrt(a) -: sqrt(b)`Apply the multiplication and division properties of square roots to simplify the expression`(\color(blue)(4)\color(red)(sqrt8)times\color(blue)(2)\color(red)(sqrt5))/(8sqrt20)` `=` `(\color(blue)(4times2)\color(red)(sqrt(8times5)))/(8sqrt20)` Multiply the coefficients by each other and the radicals by each other in the numerator `=` `(\color(blue)(8)\color(red)(sqrt(40)))/(8sqrt20)` `=` `sqrt40/sqrt20` Simplify the coefficients `=` `sqrt(40/20)` Rewrite and simplify the radicals `=` `sqrt(2)` `sqrt(2)` -
Question 2 of 6
2. Question
Simplify
`(8sqrt3times5sqrt6)/(4sqrt18)`
Correct
Nice Work!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))` or `sqrt(a -: b)=sqrt(a) -: sqrt(b)`Apply the multiplication and division properties of square roots to simplify the expression`(\color(blue)(8)\color(red)(sqrt3)times\color(blue)(5)\color(red)(sqrt6))/(4sqrt18)` `=` `(\color(blue)(8times5)\color(red)(sqrt(3times6)))/(4sqrt18)` Multiply the coefficients by each other and the radicals by each other in the numerator `=` `(\color(blue)(40)\color(red)(sqrt(18)))/(4sqrt18)` `=` `(10sqrt18)/sqrt18` Simplify the coefficients `=` `10sqrt(18/18)` Rewrite and simplify the radicals `=` `10sqrt1` `=` `10` `10` -
Question 3 of 6
3. Question
Simplify
`(4sqrt27timessqrt18)/(sqrt48)`
Correct
Nice Work!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Division Property of Square Roots
`sqrt(a/b)=(sqrt(a))/(sqrt(b))` or `sqrt(a -: b)=sqrt(a) -: sqrt(b)`Apply the multiplication and division properties of square roots to simplify the expression`(4sqrt(27)timessqrt(18))/(sqrt(48))` Reduce the radicals `=` `(4sqrt(9times3)timessqrt(9times2))/(sqrt(16times3))` Simplify `=` `(12sqrt(3)times3sqrt(2))/(4sqrt(3))` `=` `(\color(blue)(12)\color(red)(sqrt(3))times\color(blue)(3)\color(red)(sqrt(2)))/(4sqrt(3))` Multiply the coefficients by each other and the radicals by each other in the numerator `=` `(\color(blue)(12times3)\color(red)(sqrt(3times2)))/(4sqrt(3))` `=` `(\color(blue)(36)\color(red)(sqrt(6)))/(4sqrt(3))` `=` `(9sqrt(6))/sqrt(3)` Simplify the coefficients `=` `9sqrt(6/3)` Rewrite and simplify the radicals `=` `9sqrt(2)` `9sqrt(2)` -
Question 4 of 6
4. Question
Simplify`sqrt(5a^2) xx sqrt(12b^5)`Hint
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Excellent!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Combine the surds`sqrt(5a^2) xx sqrt(12b^5)` `=` `sqrt(5 xx 12 xx a^2b^5)` `=` `sqrt(60a^2b^5)` Take the perfect squares out of the surd by getting their square root`=` `sqrt(4 xx 15 xx a^2 xx b^4 xx b)` `=` `sqrt4 xx sqrt15 xx sqrt(a^2) xx sqrt(b^4) xx sqrt(b)` `=` `2 xx sqrt15 xx a xx b^2 xx sqrt(b)` `=` `2 xx a xx b^2 xx sqrt15 xx sqrt(b)` Simplify `=` `2ab^2sqrt(15b)` `2ab^2sqrt(15b)` -
Question 5 of 6
5. Question
Simplify`sqrt(7xy^2) xx 5sqrt(x)`Hint
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Exceptional!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Combine the surds`sqrt(7xy^2) xx 5sqrt(x)` `=` `5sqrt(7 xx x xx y^2 xx x)` `=` `5sqrt(7 xx x^2y^2)` Take the perfect squares out of the surd by getting their square root`=` `5 sqrt7 xx sqrt(x^2) xx sqrt(y^2)` Simplify `=` `5sqrt7 xx x xx y` `=` `5xy sqrt7` `5xy sqrt7` -
Question 6 of 6
6. Question
Simplify`sqrt(\frac{45x^3}{5x^2})`Hint
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Great Work!
Incorrect
Division Property of Surds
`sqrt(a/b)=sqrt(a) / sqrt(b)`Write as a division of separate surds`sqrt(\frac{45x^3}{5x^2})` `=` `\frac{sqrt(45) xx sqrt(x^3)}{sqrt(5) xx sqrt (x^2)}` Divide the numbers and the variables separatelyDivide the numbers`sqrt(45) / sqrt(5)` `=` `sqrt(45/5)` `=` `sqrt9` Divide the variables`sqrt(x^3) / sqrt(x^2)` `=` `sqrt((x^3)/(x^2))` `=` `sqrt(x)` Combine the simplified divisions.`=` `sqrt(9)`` xx ``sqrt(x)` Simplify `=` `3 xx sqrt(x)` `=` `3sqrt(x)` `3sqrt(x)`
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