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Simplify Roots of Negative Numbers>
Simplify Roots of Negative Numbers 2Simplify Roots of Negative Numbers 2
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Question 1 of 5
1. Question
Simplify
`sqrt(-1/9)`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root in `sqrt(-1/9)` and then simplify.`=` `color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(1/9))` Separate out the `sqrt(-1)` from the root. `=` `color(royalblue)(i)timescolor(forestgreen)(sqrt(1/9))` Replace `sqrt(-1)` with `i`. `=` `itimes1/(sqrt(9)` Simplify `sqrt(1/9)`. `=` `itimes1/3` Rearrange the answer so that the `i` is on the right-hand side. `=` `1/3i` `1/3i` -
Question 2 of 5
2. Question
Simplify
`sqrt(4-4(17))`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.First, we simplify and then try to remove the negative from the root.`=` `sqrt(4-4timescolor(royalblue)(17)` Multiply `4` and `17`. `=` `sqrt(4-color(royalblue)(68)` Subtract. `=` `sqrt(-64)` Remove the negative from the root by using `i`. `=` `isqrt(64)` Simplify `sqrt(64)`. `=` `itimes8` Rearrange the answer so that the `i` is on the right-hand side. `=` `8i` `8i` -
Question 3 of 5
3. Question
Simplify
`(4\+-sqrt(36-4(13)))/2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.Remove the negative from the root and then simplify.`(4\+-sqrt(36-color(royalblue)(4(13))))/2` Multiply `=` `(4\+-sqrt(36-color(royalblue)(52)))/2` Subtract under the root sign. `=` `(4\+-sqrt(-16))/2` Separate out the `sqrt(-1)` from the root. `=` `(4\+-sqrt(-1)timessqrt(16))/2` Replace `sqrt(-1)` with `i`. `=` `(4\+-itimessqrt(16))/2` Simplify `sqrt(16)`. `=` `(4\+-itimes4)/2` Divide both terms in the numerator by `2`. `=` `2\+-itimes 2` Rearrange the answer so that the `i` is on the right-hand side in its term. `=` `2\+-2i` `2\+-2i` -
Question 4 of 5
4. Question
Simplify
`(2+sqrt(4-164))/2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.First, we try and simplify the radical and then remove the negative from the root.`=` `(2+color(royalblue)sqrt(4-164))/2` Subtract `4-164`. `=` `(2+-color(royalblue)sqrt(-160))/2` Remove the negative root by using `i`. `=` `(2+-icolor(royalblue)sqrt(160))/2` `sqrt(160) = 4sqrt(10)`. `=` `(2+-icolor(royalblue)4sqrt(10))/2` Simplify. `=` `1+-2isqrt(10)` `1+-2isqrt(10)` -
Question 5 of 5
5. Question
Simplify
`(-6+-sqrt(16-4(16)))/2`
Correct
Great Work!
Incorrect
Imaginary numbers have the properties `i=sqrt(-1)` or `i^2=-1`.First, we try and simplify the radical and then remove the negative from the root.`=` `(-6+-color(royalblue)sqrt(16-4(16)))/2` Subtract `16-4(16)`. `=` `(-6+-color(royalblue)sqrt(-48))/2` Remove the negative root by using `i`. `=` `(-6+-icolor(royalblue)sqrt(48))/2` `sqrt(48) = 4sqrt(3)`. `=` `(-6+-icolor(royalblue)4sqrt(3))/2` Simplify. `=` `-3+-2isqrt(3)` `-3+-2isqrt(3)`
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