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Add and Subtract Surd Expressions (Basic)>
Add and Subtract Surd Expressions (Basic) 2Add and Subtract Surd Expressions (Basic) 2
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Question 1 of 4
1. Question
Simplify
`5sqrt2-sqrt18`
Hint
Correct
Great Work!
Incorrect
A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.
To simplify, the terms need to have the same radicand.`=` `5sqrt2 -color(darkviolet)(sqrt18)` Find two multiples of 18 where one is a perfect square. `=` `5sqrt2 -color(darkviolet)(sqrt9) xx sqrt2` `color(darkviolet)(9)` is a perfect square `=` `5sqrt2 -color(darkviolet)(3)sqrt2` Evaluate the coefficients of like terms (same radicand).`=` `color(royalblue)(5)color(forestgreen)(sqrt2) -color(royalblue)(3)color(forestgreen)(sqrt2)` `=` `(color(royalblue)(5-3))sqrt2` Evaluate `=` `2sqrt2` `2sqrt2` -
Question 2 of 4
2. Question
Simplify
`5sqrt3+7sqrt3-2sqrt3`
Hint
Correct
Great Work!
Incorrect
A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.Evaluate the coefficients of like terms (same radicand).`=` `color(royalblue)(5)color(forestgreen)(sqrt3) + color(royalblue)(7)color(forestgreen)(sqrt3)-color(royalblue)(2)color(forestgreen)(sqrt3)` `=` `(color(royalblue)(5+7-2))color(forestgreen)(sqrt3)` Evaluate `=` `color(royalblue)(10)sqrt3` `10sqrt3` -
Question 3 of 4
3. Question
Simplify
`4sqrt3+8sqrt3-5sqrt2`
Correct
Great Work!
Incorrect
A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.Evaluate the coefficients of like terms (same radicand).`=` `color(royalblue)(4)color(forestgreen)(sqrt3) + color(royalblue)(8)color(forestgreen)(sqrt3-5)sqrt2` `=` `(color(royalblue)(4+8))color(forestgreen)(sqrt3)-5sqrt2` Evaluate the coefficients `=` `12sqrt3-5sqrt2` `12sqrt3-5sqrt2` -
Question 4 of 4
4. Question
Simplify
`12sqrt3-sqrt3-17sqrt2`
Correct
Great Work!
Incorrect
A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.Evaluate the coefficients of like terms (same radicand).`=` `color(royalblue)(12)color(forestgreen)(sqrt3) – color(royalblue)(1)color(forestgreen)(sqrt3)-17sqrt2` `=` `(color(royalblue)(12-1))color(forestgreen)(sqrt3)-17sqrt2` Evaluate the coefficients `=` `11sqrt3-17sqrt2` `11sqrt3-17sqrt2`
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