Add and Subtract Surd Expressions 3
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Question 1 of 4
1. Question
Simplify
`10sqrt8+3sqrt12-sqrt27`
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).`=` `10sqrt8+3sqrt12-sqrt27` Find two multiples of 8, 12 and 27 each where one is a perfect square. `=` `10 xx sqrt4 xx sqrt2+3 xx sqrt4 xx sqrt3-sqrt9 xx sqrt3` Simplify `=` `10 xx 2sqrt2+3 xx 2sqrt3-3sqrt3` `4` and `9` are perfect squares `=` `20sqrt2+color(royalblue)(6)color(forestgreen)(sqrt3)-color(royalblue)(3)color(forestgreen)(sqrt3)` `=` `20sqrt2+color(royalblue)(6-3)color(forestgreen)(sqrt3)` Evaluate coefficients `=` `20sqrt2+3sqrt3` `20sqrt2+3sqrt3` -
Question 2 of 4
2. Question
Simplify
`6sqrt18+sqrt72-sqrt75`
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).`=` `6sqrt18+sqrt72-sqrt75` Find two multiples of 18, 72 and 75 each where one is a perfect square. `=` `6 xx sqrt9 xx sqrt2+sqrt36 xx sqrt2-sqrt25 xx sqrt3` Simplify `=` `6 xx 3sqrt2+6sqrt2-5sqrt3` `9`, `36` and `25` are perfect squares `=` `color(royalblue)(18)color(forestgreen)(sqrt2)+color(royalblue)(6)color(forestgreen)(sqrt2)-5sqrt3` `=` `color(royalblue)(18+6)color(forestgreen)(sqrt2)-5sqrt3` Evaluate coefficients `=` `24sqrt2-5sqrt3` `24sqrt2-5sqrt3` -
Question 3 of 4
3. Question
Simplify
`sqrt18+sqrt128-6sqrt2`
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).`=` `sqrt18+sqrt128-6sqrt2` Find two multiples of 18 and for 128 where one is a perfect square. `=` `sqrt9 xx sqrt2+sqrt64 xx sqrt2-6sqrt2` Simplify `=` `3sqrt2+8sqrt2-6sqrt2` `9` and `64` are perfect squares. `=` `color(royalblue)(3)color(forestgreen)(sqrt2)+color(royalblue)(8)color(forestgreen)(sqrt2)-color(royalblue)(6)color(forestgreen)(sqrt2)` `=` `color(royalblue)(5)color(forestgreen)(sqrt2)` Evaluate coefficients `=` `5sqrt2` `5sqrt2` -
Question 4 of 4
4. Question
Simplify
`sqrt600+sqrt150-12sqrt6`
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).`=` `sqrt600+sqrt150-12sqrt6` Find two multiples of 600 and for 150 each where one is a perfect square. `=` `sqrt100 xx sqrt6+sqrt25 xx sqrt6-12sqrt6` Simplify `=` `10sqrt6+5sqrt6-12sqrt6` `100` and `25` are perfect squares `=` `color(royalblue)(10)color(forestgreen)(sqrt6)+color(royalblue)(5)color(forestgreen)(sqrt6)-color(royalblue)(12)color(forestgreen)(sqrt6)` `=` `color(royalblue)(10+5-12)color(forestgreen)(sqrt6)` Evaluate coefficients `=` `3sqrt6` `3sqrt6`
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