Multiply Surd Expressions 2
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Question 1 of 5
1. Question
Simplify
`sqrt3 xx sqrt5`
Correct
Great Work!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a)*sqrt(b)`Apply the multiplication property of square roots to simplify the expression`sqrt3 xx sqrt5` `=` `sqrt(3 xx 5)` Multiply `=` `sqrt(15)` `sqrt(15)` -
Question 2 of 5
2. Question
Simplify
`4sqrt2 xx 6sqrt2`
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)(4)color(forestgreen)(sqrt2) xx color(royalblue)(6)color(forestgreen)(sqrt2)` Multiply numerical coefficients`color(royalblue)(4 xx 6)` `=` `24` Multiply the radicands`color(forestgreen)(sqrt2 xx sqrt2)` `=` `sqrt(4)` Combine the products`=` `24 xx sqrt(4)` Simplify `=` `24 xx 2` `4` is a perfect square `=` `48` `48` -
Question 3 of 5
3. Question
Simplify
`6sqrt8 xx 2sqrt6`
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)(6)color(forestgreen)(sqrt8) xx color(royalblue)(2)color(forestgreen)(sqrt6)` Multiply numerical coefficients`color(royalblue)(6 xx 2)` `=` `12` Multiply the radicands`color(forestgreen)(sqrt8 xx sqrt6)` `=` `sqrt(48)` Combine the products`=` `12 xx sqrt(48)` Factor by finding smaller multiples of `48` `=` `12 xx sqrt(16) xx sqrt(3)` Apply the Multiplication Property `=` `12 xx 4 xx sqrt(3)` `16` is a perfect square `=` `48sqrt(3)` `48sqrt(3)` -
Question 4 of 5
4. Question
Simplify
`8sqrt3 xx 3sqrt7`
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`color(royalblue)(8)color(forestgreen)(sqrt3) xx color(royalblue)(3)color(forestgreen)(sqrt7)` Multiply numerical coefficients`color(royalblue)(8 xx 3)` `=` `24` Multiply the radicands`color(forestgreen)(sqrt3 xx sqrt7)` `=` `sqrt(21)` Combine the products`=` `24 xx sqrt(21)` `=` `24sqrt(21)` `24sqrt(21)` -
Question 5 of 5
5. Question
Simplify
`sqrt28 xx sqrt3`
Correct
Nice Work!
Incorrect
Multiplication Property of Square Roots
`sqrt(ab)=sqrt(a)*sqrt(b)`Apply the multiplication property of square roots to simplify the expression`sqrt28 xx sqrt3` `=` `sqrt(28 xx 3)` Multiply `=` `sqrt(84)` `=` `sqrt(4 xx 21)` Factor by finding smaller multiples of `84` `=` `sqrt(4) xx sqrt(21)` Apply the Multiplication Property `=` `2 xx sqrt(21)` `4` is a perfect square `=` `2sqrt(21)` `2sqrt(21)`
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