Simplify Roots of Negative Numbers 1

Topics

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 6

Simplify

$\sqrt{- 36}$ $sqrt(-36)$

1. $3 i$ $3i$
2. $12 i$ $12i$
3. $9 i$ $9i$
4. $6 i$ $6i$

Question 2 of 6

Simplify

$\sqrt{- 5}$ $sqrt(-5)$

1. $5 i$ $5i$
2. $2.5 i$ $2.5i$
3. $i \sqrt{5}$ $isqrt(5)$
4. $\sqrt{5}$ $sqrt(5)$

Question 3 of 6

Simplify

$\sqrt{- 48}$ $sqrt(-48)$

1. $8 \sqrt{3}$ $8sqrt(3)$
2. $4 i \sqrt{3}$ $4isqrt(3)$
3. $\sqrt{3}$ $sqrt(3)$
4. $4 i$ $4i$

Question 4 of 6

Simplify

$\sqrt{- 108}$ $sqrt(-108)$

1. $\sqrt{3}$ $sqrt(3)$
2. $i \sqrt{3}$ $isqrt(3)$
3. $6 \sqrt{3}$ $6sqrt(3)$
4. $6 i \sqrt{3}$ $6isqrt(3)$

Question 5 of 6

Simplify

$\sqrt{- 10} \times \sqrt{- 15}$ $sqrt(-10) xx sqrt(-15)$

1. $5 \sqrt{6}$ $5sqrt(6)$
2. $\sqrt{6}$ $sqrt(6)$
3. $- 5 \sqrt{6}$ $-5sqrt(6)$
4. $5 i \sqrt{6}$ $5isqrt(6)$

Question 6 of 6

Simplify

$\sqrt{- \frac{1}{4}}$ $sqrt(-1/4)$

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

$=$ $=$	$\sqrt{- 1} \times \sqrt{36}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(36))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{36}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(36))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times (\sqrt{36})$ $itimes(sqrt(36))$	Simplify $\sqrt{36}$ $sqrt(36)$ .
$=$ $=$	$i \times 6$ $itimes6$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$6 i$ $6i$

$=$ $=$	$\sqrt{- 1} \times \sqrt{5}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(5))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{5}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(5))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times \sqrt{5}$ $itimessqrt(5)$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$i \sqrt{5}$ $isqrt(5)$

$=$ $=$	$\sqrt{- 1} \times \sqrt{48}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(48))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{48}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(48))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times (\sqrt{48})$ $itimes(sqrt(48))$	Simplify $\sqrt{48} = \sqrt{16} \times \sqrt{3}$ $sqrt(48) = sqrt(16) xx sqrt(3)$ .
$=$ $=$	$i \times (\sqrt{16}) \times (\sqrt{3})$ $itimes(sqrt(16))times(sqrt(3))$	Simplify `sqrt(16).
$=$ $=$	$i \times (4) \times (\sqrt{3})$ $itimes(4)times(sqrt(3))$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$4 i \sqrt{3}$ $4isqrt(3)$

$=$ $=$	$\sqrt{- 1} \times \sqrt{108}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(108))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{108}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(108))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times \sqrt{108}$ $itimessqrt(108)$	$\sqrt{108} = \sqrt{36} \times \sqrt{3}$ $sqrt(108) = sqrt(36) xx sqrt(3)$ .
$=$ $=$	$i \times (\sqrt{36}) \times (\sqrt{3})$ $itimes(sqrt(36))times(sqrt(3))$	Simplify $\sqrt{36}$ $sqrt(36)$ .
$=$ $=$	$i \times (6) \times (\sqrt{3})$ $itimes(6)times(sqrt(3))$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$6 i \sqrt{3}$ $6isqrt(3)$

$=$ $=$	$\sqrt{- 1} \times \sqrt{10} \times \sqrt{- 1} \times \sqrt{15}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(10)) xx color(accentorange)(sqrt(-1))timescolor(crimson)(sqrt(15))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{10} \times i \times \sqrt{15}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(10)) xx color(accentorange)(i)timescolor(crimson)(sqrt(15))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times (\sqrt{5} \times \sqrt{2}) \times i \times (\sqrt{5} \times \sqrt{3})$ $itimes(sqrt(5) xx sqrt(2)) xx itimes(sqrt(5) xx sqrt(3))$	$\sqrt{10} = \sqrt{5} \times \sqrt{2}$ $sqrt(10) = sqrt(5) xx sqrt(2)$ and $\sqrt{15} = \sqrt{5} \times \sqrt{3}$ $sqrt(15) = sqrt(5) xx sqrt(3)$ .
$=$ $=$	$- 1 \times 5 \times \sqrt{6}$ $-1times5timessqrt(6)$	Simplify.
$=$ $=$	$- 5 \sqrt{6}$ $-5sqrt(6)$

Simplify Roots of Negative Numbers 1

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!

6. Question

Great Work!

Quizzes

$=$ $=$	$\sqrt{- 1} \times \sqrt{\frac{1}{4}}$ $color(royalblue)(sqrt(-1))timescolor(forestgreen)(sqrt(1/4))$	Separate out the $\sqrt{- 1}$ $sqrt(-1)$ from the root.
$=$ $=$	$i \times \sqrt{\frac{1}{4}}$ $color(royalblue)(i)timescolor(forestgreen)(sqrt(1/4))$	Replace $\sqrt{- 1}$ $sqrt(-1)$ with $i$ $i$ .
$=$ $=$	$i \times \frac{1}{\sqrt{4}}$ $itimes1/(sqrt(4)$	Simplify $\sqrt{\frac{1}{4}}$ $sqrt(1/4)$ .
$=$ $=$	$i \times \frac{1}{2}$ $itimes1/2$	Rearrange the answer so that the $i$ $i$ is on the right-hand side.
$=$ $=$	$\frac{1}{2} i$ $1/2i$