Multiply Surd Expressions 3
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
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 Surds with Variables 1
- Simplify Surds with Variables 2
- Simplify Surds with Variables 3
- Rewriting Entire and Mixed Surds 1
- Rewriting Entire and Mixed Surds 2
- Add and Subtract Surd Expressions (Basic) 1
- Add and Subtract Surd Expressions (Basic) 2
- Add and Subtract Surd Expressions (Basic) 3
- Add and Subtract Surd Expressions 1
- Add and Subtract Surd Expressions 2
- Add and Subtract Surd Expressions 3
- Multiply Surd Expressions 1
- Multiply Surd Expressions 2
- Multiply Surd Expressions 3
- Multiply Surd Expressions 4
- Divide Surd Expressions 1
- Divide Surd Expressions 2
- Divide Surd Expressions 3
- Multiply and Divide Surd Expressions
- Simplify Surd Expressions using the Distributive Property 1
- Simplify Surd Expressions using the Distributive Property 2
- Simplify Surd Expressions using the Distributive Property 3
- Simplify Binomial Surd Expressions using the FOIL Method 1
- Simplify Binomial Surd Expressions using the FOIL Method 2
- Rationalising the Denominator 1
- Rationalising the Denominator 2
- Rationalising the Denominator 3
- Rationalising the Denominator 4
- Rationalising the Denominator using Conjugates