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Simplify Binomial Surd Expressions using the FOIL Method>
Simplify Binomial Surd Expressions using the FOIL Method 2Simplify Binomial Surd Expressions using the FOIL Method 2
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Question 1 of 4
1. Question
Simplify
`(10sqrt2-sqrt3) (4sqrt2+2sqrt3)`
Correct
Excellent!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`(color(darkviolet)(a)+color(royalblue)(b)) (color(forestgreen)(c)+color(crimson)(d))=color(darkviolet)(a)color(forestgreen)(c)+color(darkviolet)(a)color(crimson)(d)+color(royalblue)(b)color(forestgreen)(c)+color(royalblue)(b)color(crimson)(d)`Apply the Distributive Property.`=` `(color(darkviolet)(10sqrt2)-color(royalblue)(sqrt3)) (color(forestgreen)(4sqrt2)+color(crimson)(2sqrt3))` `=` `color(darkviolet)(10sqrt2) xx color(forestgreen)(4sqrt2)+color(darkviolet)(10sqrt2) xx color(crimson)(2sqrt3)-color(royalblue)(sqrt3) xx color(forestgreen)(4sqrt2)-color(royalblue)(sqrt3) xx color(crimson)(2sqrt3)` `=` `40sqrt4 +20sqrt6 – 4sqrt6-2sqrt9` Simplify the Surds `=` `40 xx 2 + 20 xx sqrt6 – 4 xx sqrt6 – 2 xx 3` Multiplying `=` `80 + 20 xx sqrt6 – 4 xx sqrt6-6` Combine like Terms `=` `74+16sqrt6` `74+16sqrt6` -
Question 2 of 4
2. Question
Simplify
`(7-2sqrt3) (6sqrt3+5)`
Correct
Excellent!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`(color(darkviolet)(a)+color(royalblue)(b)) (color(forestgreen)(c)+color(crimson)(d))=color(darkviolet)(a)color(forestgreen)(c)+color(darkviolet)(a)color(crimson)(d)+color(royalblue)(b)color(forestgreen)(c)+color(royalblue)(b)color(crimson)(d)`Apply the Distributive Property.`=` `(color(darkviolet)(7)-color(royalblue)(2sqrt3)) (color(forestgreen)(6sqrt3)+color(crimson)(5))` `=` `color(darkviolet)(7) xx color(forestgreen)(6sqrt3)+color(darkviolet)(7) xx color(crimson)(5)-color(royalblue)(2sqrt3) xx color(forestgreen)(6sqrt3)-color(royalblue)(2sqrt3) xx color(crimson)(5)` `=` `42sqrt3 +35-12sqrt9-10sqrt3` Simplify the Surds `=` `42sqrt3 +35-12 xx 3-10sqrt3` Multiplying `=` `42sqrt3 +35-36-10sqrt3` Combine like Terms `=` `32sqrt3 – 1` `32sqrt3 – 1` -
Question 3 of 4
3. Question
Simplify
`(3sqrt2+sqrt6)^2`
Correct
Excellent!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`(color(darkviolet)(a)+color(royalblue)(b)) (color(forestgreen)(c)+color(crimson)(d))=color(darkviolet)(a)color(forestgreen)(c)+color(darkviolet)(a)color(crimson)(d)+color(royalblue)(b)color(forestgreen)(c)+color(royalblue)(b)color(crimson)(d)`Apply the Distributive Property.`=` `(color(darkviolet)(3sqrt2)+color(royalblue)(sqrt6)) (color(forestgreen)(3sqrt2)+color(crimson)(sqrt6))` `=` `color(darkviolet)(3sqrt2) xx color(forestgreen)(3sqrt2)+color(darkviolet)(3sqrt2) xx color(crimson)(sqrt6)+color(royalblue)(sqrt6) xx color(forestgreen)(3sqrt2)+color(royalblue)(sqrt6) xx color(crimson)(sqrt6)` `=` `9sqrt4 + 3 xx 2sqrt3 + 3 xx 2sqrt3+sqrt36` Simplify the Surds `=` `9 xx 2 + 3 xx 2sqrt3 + 3 xx 2sqrt3 + 6` Multiplying `=` `18 + 6sqrt3 + 6sqrt3 + 6` Combine like Terms `=` `24+12sqrt3` `24+12sqrt3` -
Question 4 of 4
4. Question
Simplify
`(5sqrt3+2sqrt2)^2`
Correct
Excellent!
Incorrect
Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Distributive Property
`(color(darkviolet)(a)+color(royalblue)(b)) (color(forestgreen)(c)+color(crimson)(d))=color(darkviolet)(a)color(forestgreen)(c)+color(darkviolet)(a)color(crimson)(d)+color(royalblue)(b)color(forestgreen)(c)+color(royalblue)(b)color(crimson)(d)`Apply the Distributive Property.`=` `(color(darkviolet)(5sqrt3)+color(royalblue)(2sqrt2)) (color(forestgreen)(5sqrt3)+color(crimson)(2sqrt2))` `=` `color(darkviolet)(5sqrt3) xx color(forestgreen)(5sqrt3)+color(darkviolet)(5sqrt3) xx color(crimson)(2sqrt2)+color(royalblue)(2sqrt2) xx color(forestgreen)(5sqrt3)+color(royalblue)(2sqrt2) xx color(crimson)(2sqrt2)` `=` `25 xx 3 + 10sqrt6 + 10sqrt6+4 xx 2` Multiplying `=` `75 + 10sqrt6 + 10sqrt6+ 8` Combine like Terms `=` `83 + 20sqrt6` `83 + 20sqrt6`
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