Question

sqrt -48 simplify the following expression express in terms of i

Answer 1

sqrt(xy) = sqrt(x)*sqrt(y)

i = sqrt(-1)

Any guesses what to do next?

Answer 2

Multiply

Answer 3

Multiply what? use the info from the problem.

Answer 4

Nm it would be to divide right?

Answer 5

bc when I tried finding the sqrt it was a decimal

Answer 6

You can't use a calculator to solve this problem.

What you need to do is factor out the square root.

sqrt(28) = 2*sqrt(7) because sqrt (28) is equal to sqrt(4)*sqrt(7) = sqrt(4*7) = sqrt(28)

Answer 7

Or you would do (-1)6*8=48

Answer 8

Yes, you're getting closer :)

Answer 9

Ugh I am stuck

Answer 10

So would I then break down the 8?

Answer 11

and the 6?

Answer 12

You're not stuck, you are so close. You have to factor out numbers that can be broken down by square roots. Like in my example of sqrt(28), I pulled out the 4 because sqrt(4) = 2

Answer 13

You can't get a sqrt of 6 or 8. But what factors of 48 CAN be broken down by a square root?

Answer 14

4?

Answer 15

Yes, that's one. But there is a greater factor...

Answer 16

12

Answer 17

Yes, but you can't get a sqrt of 12... a little higher

Think only in terms of numbers that are squares...

Answer 18

16

Answer 19

YES! :)

Answer 20

Yay! So how can I write it out??

Answer 21

So, 16 is the biggest factor of 48 that will help us here.

16*3 = 48

-1*16*3 = -48

Here's our problem, what is sqrt(-48)

Well, sqrt(-48) = sqrt(-1*16*3)

What's next?

Answer 22

-1*8*3^2?

Answer 23

Not quite. Use this rule,

sqrt(a*b) = sqrt(a)*sqrt(b)

Answer 24

16*3?

Answer 25

Ohh!!!! Ok hang on!

Answer 26

Ok so I got a big #

Answer 27

2304 which doesnt look right

Answer 28

No that's not correct.

If sqrt(a*b) = sqrt(a)*sqrt(b), what does sqrt(-1*16*3) = ???

Answer 29

-48

Answer 30

Sorry I told you im not good at this ;/

Answer 31

It's ok.

You are trying to pull the -1, 16, and 3 out of the sqrt.

If sqrt(a*b) = sqrt(a)*sqrt(b), then for example sqrt(4*7) = sqrt(4)*sqrt(7)

Answer 32

one sqrt becomes two sqrts

Answer 33

I got 4 for sqrt 16

Answer 34

Right. But what is the whole thing?

If sqrt(a*b*c) = sqrt(a)*sqrt(b)*sqrt(c) then,

sqrt(-1*16*3) = sqrt(-1)*sqrt(16)*sqrt(3) right?

Answer 35

Yes

Answer 36

So then that would be 0

Answer 37

zero? where are you getting zero?

Answer 38

By putting sqrt after the numbers the calculator zeroed it out

Answer 39

Put the calculator down :)

Answer 40

You do not need it at all. Trust me.

Answer 41

LOL ok

Answer 42

Ok, so we know that sqrt(-48) = sqrt(-1)*sqrt(16)*sqrt(3) right?

Answer 43

Right. So do we add or subtract at all?

Answer 44

There is no addition or subtraction in this problem. Don't look for things that aren't there.

Answer 45

What you have is sqrt(-48) = sqrt(-1)*sqrt(16)*sqrt(3)

Simplify.

Answer 46

[You already told me sqrt(16) is 4, so 4*sqrt(-1)*sqrt(3)]

Answer 47

so simplifying 4 would be 2

Answer 48

4 is already simplified. 4 is the sqrt of 16

Answer 49

you can't make 4 simpler than 4 :)

Answer 50

Oh ok oops

Answer 51

So it would then be sqrt 4 right?

Answer 52

It's ok, this isn't simple stuff.

There's only two things left that might be able to be simplified:

sqrt(-1) and sqrt(3)

Can you simplify one of these? both?

Answer 53

No 4 is already simplified. Ignore 4. that's done.

Answer 54

You can't simplify 3 or -1

Answer 55

You are half right.

You cannot simplify sqrt(3)

But, what is sqrt(-1) ???

Answer 56

1! ;)

Answer 57

No, that's not correct.

A square root is a number when multiplied by itself equals the square. So basically, you are saying that 1 times 1 equals -1.

Answer 58

Let me ask you this question...

what is i ??

Answer 59

sqrt of -1 =i

Answer 60

Exactly. So what is the sqrt(-1) ???

Answer 61

i

Answer 62

Perfect :)

Answer 63

So the answer is 4i

Answer 64

What happened to that sqrt(3) ???

Answer 65

Don't forget it.

Answer 66

So, hears your answer:

sqrt(-48) = sqrt(16*-1*3) = sqrt(16)*sqrt(-1)*sqrt(3) = 4i*sqrt(3)

Answer 67

4i*sqrt(3) is the final answer

Answer 68

I got it!!! Thank you soooo much!!!

Answer 69

You're welcome :)