Multiply Radical Expressions 3
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Question 1 of 5
1. Question
Simplify
`4sqrt18 xx 6sqrt5`
Correct
Correct!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Multiply the coefficients and then the radicands of each term`color(royalblue)(4)color(forestgreen)(sqrt18) xx color(royalblue)(6)color(forestgreen)(sqrt5)` Multiply numerical coefficients`color(royalblue)(4 xx 6)` `=` `24` Multiply the radicands`color(forestgreen)(sqrt18 xx sqrt5)` `=` `sqrt(90)` Combine the products`=` `24 xx sqrt(90)` Factor by finding smaller multiples of `48` `=` `24 xx sqrt(9) xx sqrt(10)` Apply the Multiplication Property `=` `24 xx 3 xx sqrt(10)` `9` is a perfect square `=` `72sqrt(10)` `72sqrt(10)` -
Question 2 of 5
2. Question
Simplify
`7sqrt6 xx 2sqrt8`
Correct
Good Job!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Multiply the coefficients and then the radicands of each term`color(royalblue)(7)color(forestgreen)(sqrt6) xx color(royalblue)(2)color(forestgreen)(sqrt8)` Multiply numerical coefficients`color(royalblue)(7 xx 2)` `=` `14` Multiply the radicands`color(forestgreen)(sqrt6 xx sqrt8)` `=` `sqrt(48)` Combine the products`=` `14 xx sqrt(48)` Factor by finding smaller multiples of `48` `=` `14 xx sqrt(16) xx sqrt(3)` Apply the Multiplication Property `=` `14 xx 4 xx sqrt(3)` `16` is a perfect square `=` `56sqrt(3)` `56sqrt(3)` -
Question 3 of 5
3. Question
Simplify
`2sqrt6 xx 6sqrt3`
Correct
Fantastic!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Multiply the coefficients and then the radicands of each term`color(royalblue)(2)color(forestgreen)(sqrt6) xx color(royalblue)(6)color(forestgreen)(sqrt3)` Multiply numerical coefficients`color(royalblue)(2 xx 6)` `=` `12` Multiply the radicands`color(forestgreen)(sqrt6 xx sqrt3)` `=` `sqrt(18)` Combine the products`=` `12 xx sqrt(18)` Factor by finding smaller multiples of `18` `=` `12 xx sqrt(9) xx sqrt(2)` Apply the Multiplication Property `=` `12 xx 3 xx sqrt(2)` `36` is a perfect square `=` `36sqrt(2)` `36sqrt(2)` -
Question 4 of 5
4. Question
Simplify
`4sqrt3 xx 2sqrt3 xx sqrt2`
Correct
Excellent!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Multiply the coefficients and then the radicands of each term. Remember that if there’s no radicand, the radicand is `1`.`color(royalblue)(4)color(forestgreen)(sqrt3) xx color(royalblue)(2)color(forestgreen)(sqrt3) xx color(royalblue)(1)color(forestgreen)(sqrt2)` Multiply numerical coefficients`color(royalblue)(4 xx 2 xx 1)` `=` `8` Multiply the radicands`color(forestgreen)(sqrt3 xx sqrt3 xx sqrt2)` `=` `sqrt(18)` Combine the products`=` `8 xx sqrt(18)` Factor by finding smaller multiples of `18` `=` `8 xx sqrt(9) xx sqrt(2)` Apply the Multiplication Property `=` `8 xx 3 xx sqrt(2)` `9` is a perfect square `=` `24sqrt(2)` `24sqrt(2)` -
Question 5 of 5
5. Question
Simplify
`5sqrt6 xx 2sqrt5 xx 3sqrt2`
Correct
Well Done!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a) xx sqrt(b)`Multiply the coefficients and then the radicands of each term`color(royalblue)(5)color(forestgreen)(sqrt6) xx color(royalblue)(2)color(forestgreen)(sqrt5) xx color(royalblue)(3)color(forestgreen)(sqrt2)` Multiply numerical coefficients`color(royalblue)(5 xx 2 xx 3)` `=` `30` Multiply the radicands`color(forestgreen)(sqrt6 xx sqrt5 xx sqrt2)` `=` `sqrt(60)` Combine the products`=` `30 xx sqrt(60)` Factor by finding smaller multiples of `60` `=` `30 xx sqrt(4) xx sqrt(15)` Apply the Multiplication Property `=` `30 xx 2 xx sqrt(15)` `4` is a perfect square `=` `60sqrt(15)` `60sqrt(15)`
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