Simplify Roots of Negative Numbers 2

Question 1 of 5

Simplify

$\sqrt{- \frac{1}{9}}$ $sqrt(-1/9)$

1. $3 i$ $3i$
2. $\frac{1}{3} i$ $1/3i$
3. $\frac{1}{3} i$ $1/3i$
4. $3 i$ $3i$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Imaginary numbers have the properties

i = \sqrt{- 1}

$i=sqrt(-1)$ or

i^{2} = - 1

$i^2=-1$ .

Remove the negative from the root in

\sqrt{- \frac{1}{9}}

$sqrt(-1/9)$ and then simplify.

$=$ $=$	$\sqrt{- 1} \times \sqrt{\frac{1}{9}}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(1/9))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{\frac{1}{9}}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(1/9))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times \frac{1}{\sqrt{9}}$ $itimes1/(sqrt(9)$	Simplify $\sqrt{\frac{1}{9}}$ $sqrt(1/9)$ .
$=$ $=$	$i \times \frac{1}{3}$ $itimes1/3$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$\frac{1}{3} i$ $1/3i$

\frac{1}{3} i

$1/3i$

Question 2 of 5

Simplify

$\sqrt{4 - 4 (17)}$ $sqrt(4-4(17))$

1. $8 i$ $8i$
2. $64 i$ $64i$
3. $4 i$ $4i$
4. $- 16 i$ $-16i$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Imaginary numbers have the properties

i = \sqrt{- 1}

$i=sqrt(-1)$ or

i^{2} = - 1

$i^2=-1$ .

First, we simplify and then try to remove the negative from the root.

$=$ $=$	$\sqrt{4 - 4 \times 17}$ $sqrt(4-4timescolor(royalblue)(17)$	Multiply $4$ $4$ and $17$ $17$ .
$=$ $=$	$\sqrt{4 - 68}$ $sqrt(4-color(royalblue)(68)$	Subtract.
$=$ $=$	$\sqrt{- 64}$ $sqrt(-64)$	Remove the negative from the root by using $i$ $i$ .
$=$ $=$	$i \sqrt{64}$ $isqrt(64)$	Simplify $\sqrt{64}$ $sqrt(64)$ .
$=$ $=$	$i \times 8$ $itimes8$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$8 i$ $8i$

8 i

$8i$

Question 3 of 5

Simplify

$\frac{4 \pm \sqrt{36 - 4 (13)}}{2}$ $(4\+-sqrt(36-4(13)))/2$

1. $4 \pm 4 i$ $4\+-4i$
2. $2 \pm 2 i$ $2\+-2i$
3. $4 \pm 2 i$ $4\+-2i$
4. $2 \pm 4 i$ $2\+-4i$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Imaginary numbers have the properties

i = \sqrt{- 1}

$i=sqrt(-1)$ or

i^{2} = - 1

$i^2=-1$ .

Remove the negative from the root and then simplify.

	$\frac{4 \pm \sqrt{36 - 4 (13)}}{2}$ $(4\+-sqrt(36-color(royalblue)(4(13))))/2$	Multiply
$=$ $=$	$\frac{4 \pm \sqrt{36 - 52}}{2}$ $(4\+-sqrt(36-color(royalblue)(52)))/2$	Subtract under the root sign.
$=$ $=$	$\frac{4 \pm \sqrt{- 16}}{2}$ $(4\+-sqrt(-16))/2$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$\frac{4 \pm \sqrt{- 1} \times \sqrt{16}}{2}$ $(4\+-sqrt(-1)timessqrt(16))/2$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$\frac{4 \pm i \times \sqrt{16}}{2}$ $(4\+-itimessqrt(16))/2$	Simplify $\sqrt{16}$ $sqrt(16)$ .
$=$ $=$	$\frac{4 \pm i \times 4}{2}$ $(4\+-itimes4)/2$	Divide both terms in the numerator by $2$ $2$ .
$=$ $=$	$2 \pm i \times 2$ $2\+-itimes 2$	Rearrange the answer so that the $i$ $i$ is on the right-hand side in its term.
$=$ $=$	$2 \pm 2 i$ $2\+-2i$

2 \pm 2 i

$2\+-2i$

Question 4 of 5

Simplify

$\frac{2 + \sqrt{4 - 164}}{2}$ $(2+sqrt(4-164))/2$

1. $1 \pm 2 i \sqrt{10}$ $1+-2isqrt(10)$
2. $1 \pm 2 \sqrt{10}$ $1+-2sqrt(10)$
3. $1 \pm 2 i$ $1+-2i$
4. $1 \pm i \sqrt{10}$ $1+-isqrt(10)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Imaginary numbers have the properties

i = \sqrt{- 1}

$i=sqrt(-1)$ or

i^{2} = - 1

$i^2=-1$ .

First, we try and simplify the radical and then remove the negative from the root.

$=$ $=$	$\frac{2 + \sqrt{4 - 164}}{2}$ $(2+color(royalblue)sqrt(4-164))/2$	Subtract $4 - 164$ $4-164$ .
$=$ $=$	$\frac{2 \pm \sqrt{- 160}}{2}$ $(2+-color(royalblue)sqrt(-160))/2$	Remove the negative root by using $i$ $i$ .
$=$ $=$	$\frac{2 \pm i \sqrt{160}}{2}$ $(2+-icolor(royalblue)sqrt(160))/2$	$\sqrt{160} = 4 \sqrt{10}$ $sqrt(160) = 4sqrt(10)$ .
$=$ $=$	$\frac{2 \pm i 4 \sqrt{10}}{2}$ $(2+-icolor(royalblue)4sqrt(10))/2$	Simplify.
$=$ $=$	$1 \pm 2 i \sqrt{10}$ $1+-2isqrt(10)$

1 \pm 2 i \sqrt{10}

$1+-2isqrt(10)$

Question 5 of 5

Simplify

$\frac{- 6 \pm \sqrt{16 - 4 (16)}}{2}$ $(-6+-sqrt(16-4(16)))/2$

1. $- 3 \pm 2 i$ $-3+-2i$
2. $3 \pm 2 i \sqrt{3}$ $3+-2isqrt(3)$
3. $3 \pm 2 i$ $3+-2i$
4. $- 3 \pm 2 i \sqrt{3}$ $-3+-2isqrt(3)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

Imaginary numbers have the properties

i = \sqrt{- 1}

$i=sqrt(-1)$ or

i^{2} = - 1

$i^2=-1$ .

First, we try and simplify the radical and then remove the negative from the root.

$=$ $=$	$\frac{- 6 \pm \sqrt{16 - 4 (16)}}{2}$ $(-6+-color(royalblue)sqrt(16-4(16)))/2$	Subtract $16 - 4 (16)$ $16-4(16)$ .
$=$ $=$	$\frac{- 6 \pm \sqrt{- 48}}{2}$ $(-6+-color(royalblue)sqrt(-48))/2$	Remove the negative root by using $i$ $i$ .
$=$ $=$	$\frac{- 6 \pm i \sqrt{48}}{2}$ $(-6+-icolor(royalblue)sqrt(48))/2$	$\sqrt{48} = 4 \sqrt{3}$ $sqrt(48) = 4sqrt(3)$ .
$=$ $=$	$\frac{- 6 \pm i 4 \sqrt{3}}{2}$ $(-6+-icolor(royalblue)4sqrt(3))/2$	Simplify.
$=$ $=$	$- 3 \pm 2 i \sqrt{3}$ $-3+-2isqrt(3)$

- 3 \pm 2 i \sqrt{3}

$-3+-2isqrt(3)$

Simplify Roots of Negative Numbers 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Great Work!

2. Question

Great Work!

3. Question

Great Work!

4. Question

Great Work!

5. Question

Great Work!

Quizzes