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Add and Subtract Radical Expressions (Basic)>
Add and Subtract Radical Expressions (Basic) 2Add and Subtract Radical 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 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