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Simplify Roots of Negative Numbers>
Simplify Roots of Negative Numbers 1Simplify Roots of Negative Numbers 1
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Question 1 of 6
1. Question
Simplify
`sqrt(-36)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-36)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(36))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(36))` Replace `sqrt(-1)` with `i`. `=` `itimes(sqrt(36))` Simplify `sqrt(36)`. `=` `itimes6` Rearrange the answer so that the `i` is on the right-hand side. `=` `6i` `6i` -
Question 2 of 6
2. Question
Simplify
`sqrt(-5)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-5)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(5))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(5))` Replace `sqrt(-1)` with `i`. `=` `itimessqrt(5)` Rearrange the answer so that the `i` is on the right-hand side. `=` `isqrt(5)` `isqrt(5)` -
Question 3 of 6
3. Question
Simplify
`sqrt(-48)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-48)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(48))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(48))` Replace `sqrt(-1)` with `i`. `=` `itimes(sqrt(48))` Simplify `sqrt(48) = sqrt(16) xx sqrt(3)`. `=` `itimes(sqrt(16))times(sqrt(3))` Simplify `sqrt(16). `=` `itimes(4)times(sqrt(3))` Rearrange the answer so that the `i` is on the right-hand side. `=` `4isqrt(3)` `4isqrt(3)` -
Question 4 of 6
4. Question
Simplify
`sqrt(-108)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-108)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(108))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(108))` Replace `sqrt(-1)` with `i`. `=` `itimessqrt(108)` `sqrt(108) = sqrt(36) xx sqrt(3)`. `=` `itimes(sqrt(36))times(sqrt(3))` Simplify `sqrt(36)`. `=` `itimes(6)times(sqrt(3))` Rearrange the answer so that the `i` is on the right-hand side. `=` `6isqrt(3)` `6isqrt(3)` -
Question 5 of 6
5. Question
Simplify
`sqrt(-10) xx sqrt(-15)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-10)` and `sqrt(-15)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(10)) xx color(accentorange)(sqrt(-1))timescolor(crimson)(sqrt(15))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(10)) xx color(accentorange)(i)timescolor(crimson)(sqrt(15))` Replace `sqrt(-1)` with `i`. `=` `itimes(sqrt(5) xx sqrt(2)) xx itimes(sqrt(5) xx sqrt(3))` `sqrt(10) = sqrt(5) xx sqrt(2)` and `sqrt(15) = sqrt(5) xx sqrt(3)`. `=` `-1times5timessqrt(6)` Simplify. `=` `-5sqrt(6)` `-5sqrt(6)` -
Question 6 of 6
6. Question
Simplify
`sqrt(-1/4)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-1/4)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(1/4))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(1/4))` Replace `sqrt(-1)` with `i`. `=` `itimes1/(sqrt(4)` Simplify `sqrt(1/4)`. `=` `itimes1/2` Rearrange the answer so that the `i` is on the right-hand side. `=` `1/2i` `1/2i`
Quizzes
- Simplify Roots of Negative Numbers 1
- Simplify Roots of Negative Numbers 2
- Powers of the Imaginary Unit 1
- Powers of the Imaginary Unit 2
- Solve Quadratic Equations with Complex Solutions 1
- Solve Quadratic Equations with Complex Solutions 2
- Equality of Complex Numbers
- Add and Subtract Complex Numbers 1
- Add and Subtract Complex Numbers 2
- Multiply Complex Numbers 1
- Multiply Complex Numbers 2
- Divide Complex Numbers
- Complex Numbers – Product of Linear Factors 1
- Complex Numbers – Product of Linear Factors 2
- Mixed Operations with Complex Numbers