Question

Which expression is equivalent to

21 + square root(-36)

Answer 1

help

Answer 2

Which?
Do we have some options?

Answer 3

yes

Answer 4

You can simplify the radical.
\[\Large\rm \sqrt{-36}=\sqrt{-1\cdot 36}=\sqrt{-1}\cdot \sqrt{36}=\mathcal i \sqrt{36}\]Is 36 a prefect square? Can we take it's root?

Answer 5

27i

21 + 6i

21 - 6i

21i

Answer 6

no and yes

Answer 7

lol that should have been yes and yes you silly billy ^^

Answer 8

6*6 is 36 yes?
So sqrt36 = 6

Answer 9

lol

Answer 10

thats it

Answer 11

Hmm so which option does it look like? :U

Answer 12

c

Answer 13

21-6i

Answer 14

Hmm why the subtraction? :o

Answer 15

u change signs

Answer 16

\[\Large\rm =21 + \sqrt{-36}\]\[\Large\rm =21 + \sqrt{-1}\cdot \sqrt{36}\]The negative is what's turning into the i,\[\Large\rm =21 + \mathcal i\cdot \sqrt{36}\]So we shouldn't have a negative anymore.
Not sure what you meant by `change signs` :d

Answer 17

okay thanks thats much better

Answer 18

Simplify the following expression: i2 X i5

Answer 19

Are those exponents or not?\[\Large\rm \mathcal i^2\cdot \mathcal i^5\]

Answer 20

yes

Answer 21

sorry

Answer 22

Applying rules of exponents:\[\Large\rm \color{royalblue}{x^a\cdot x^b=x^{a+b}}\]See how we can use this rule?

Answer 23

yes

Answer 24

how can we use this rule

Answer 25

You said yes -_-
I thought you had it...
\[\Large\rm \mathcal i^2\cdot \mathcal i^5=\mathcal i ^{2+5}=\mathcal i^{7}\]

Now this next part is a little tricky...
Since we have a power on i greater than 4, it means this can be simplified.

Answer 26

okay so it will be i

Answer 27

Let's back up to the original problem...

\[\Large\rm \mathcal i^2\cdot \mathcal i^5\]Powers of i will repeat over and over.
Every 4th power.

So i^5 is the same as i^1
That tells us that i^5=i

Our problem simplifies to:
\[\Large\rm \mathcal i^2\cdot \mathcal i\]Do you understand how to calculate i^2?

Answer 28

yes ik that part

Answer 29

i^2 is -1 right?

So it looks like we end up with:\[\Large\rm -1\cdot \mathcal i=-\mathcal i\]Powers of i can be pretty tricky! :(

Answer 30

yes ik i had trouble with these problems

Answer 31

Which expression is equivalent to

21 + square root(-36)

Answer 32

A sphere has a diameter of 4 meters. What is the approximate volume of the sphere.