Simplify Square Roots 3
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Question 1 of 5
1. Question
Simplify.`sqrt(108)`Hint
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`To simplify `sqrt(108)`, find factors that are perfect squares`sqrt(108)` `=` `sqrt(36 xx 3)` Factor by finding smaller multiples of `108` `=` `sqrt(36) xx sqrt(3)` Apply the Radical Multiplication Property `=` `6 xx sqrt(3)` `36` is a perfect square `=` `6sqrt(3)` `6sqrt(3)` -
Question 2 of 5
2. Question
Simplify`sqrt432`Hint
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`To simplify `sqrt(432)`, find factors that are perfect squares`sqrt(432)` `=` `sqrt(144 xx 3)` Factor by finding smaller multiples of `432` `=` `sqrt(144) xx sqrt(3)` Apply the Radical Multiplication Property `=` `12 xx sqrt(3)` `144` is a perfect square `=` `12sqrt(3)` `12sqrt(3)` -
Question 3 of 5
3. Question
Simplify`3sqrt200`Hint
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, you can separate the coefficient from the square root.`3sqrt(200)` `=` `3 xx sqrt(200)` Next, to simplify `sqrt(200)`, find factors that are perfect squares`3 xx sqrt(200)` `=` `3 xx sqrt(100xx2)` Factor by finding smaller multiples of `432` `=` `3 xx sqrt(100) xx sqrt(2)` Apply the Radical Multiplication Property `=` `3 xx 10 xx sqrt(2)` `100` is a perfect square `=` `30 xx sqrt(2)` `=` `30sqrt(2)` `30sqrt(2)` -
Question 4 of 5
4. Question
Simplify`8sqrt48`Hint
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, you can separate the coefficient from the square root.`8sqrt(48)` `=` `8 xx sqrt(48)` Next, to simplify `sqrt(48)`, find factors that are perfect squares`8 xx sqrt(48)` `=` `8 xx sqrt(16xx3)` Factor by finding smaller multiples of `48` `=` `8 xx sqrt(16) xx sqrt(3)` Apply the Radical Multiplication Property `=` `8 xx 4 xx sqrt(3)` `16` is a perfect square `=` `32 xx sqrt(3)` `=` `32sqrt(3)` Alternatively, you can use other square factors of `48` and get the same simplified value. Take note that the process will be longer if you are not using the highest square factor.`8 xx sqrt(48)` `=` `8 xx sqrt(4xx12)` `4` and `12` are factors of `48` `=` `8 xx sqrt(4) xx sqrt(12)` Apply the Radical Multiplication Property `=` `8 xx 2 xx sqrt(12)` `4` is a perfect square `=` `16 xx sqrt(4xx3)` `4` and `3` are factors of `12` `=` `16 xx sqrt(4) xx sqrt(3)` Apply the Radical Multiplication Property `=` `16 xx 2 xx sqrt(3)` `4` is a perfect square `=` `32 xx sqrt(3)` `=` `32sqrt(3)` `32sqrt(3)` -
Question 5 of 5
5. Question
Simplify
`sqrt63`
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Multiplication Property of Radicals
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, find the largest perfect square that divides evenly into `63 \ color(forestgreen)((9))``sqrt(63)` `=` `sqrt(color(forestgreen)(9) xx 7)` `9` is a perfect square `=` `sqrt(color(forestgreen)(9)) xx sqrt(7)` Apply the Multiplication Property `=` `color(forestgreen)(9) xx sqrt(7)` `color(forestgreen)(sqrt(9)=3)` `=` `3sqrt(7)` `3sqrt(7)`
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