Question

how do you simplify the following expression?
square root of -144 square root of -48

Answer 1

\[x=\sqrt{-144}=+-12 i\]

Answer 2

how sis you do that i dont understand

Answer 3

i is iota used for defining imaginary numbers...as such no real numbers can define sqrt of a negative number

Answer 4

i m not your sis...siisy

Answer 5

sorry ment did

Answer 6

The s is right next to the d on an azerty keyboard. It must have been an accident indeed :-)

Answer 7

can you explain it a little better I think that person got mad and I didnt mean to mae them mad

Answer 8

oops make

Answer 9

these two dont have anything between them. it is sqrt-144sqrt-48

Answer 10

is it
\[ \sqrt{-144}\sqrt{-48} \]

Answer 11

yes

Answer 12

http://en.wikipedia.org/wiki/Square_root#Square_roots_of_negative_and_complex_numbers

√-144=√-1 * √144 = +-i * 12
√-48 = √-1 * √48 = +-i * √48

Answer 13

so you are multiplying two square roots. First notice that they are negative (that means you will get an imaginary number)

write them as
\[ \sqrt{144}\sqrt{-1}\sqrt{48}\sqrt{-1} \]
the sqrt(-1) is called i ("i" for imaginary")
you are multiplying, so you can change the order (example:2*3 is the same as 3*2)
\[ \sqrt{144}\sqrt{48}\sqrt{-1}\sqrt{-1} \]
now simplify: what is the sqrt(144) (it is a whole number)

Answer 14

ok 144 is 12 and not sure what 48 is

Answer 15

I dont think there is one for 48

Answer 16

\[4\sqrt{3}\]

Answer 17

to simplify 48, the easiest way (other than memorizing things) is factor it into its prime factors: first divide by 2
2 * 24
2 * 2*12
2*2*2*6
2*2*2*2*3
now look for pairs of numbers. here you have two pairs of 2's
(2*2)*(2*2)*3
"pull out" the 2 pair from the square root
sqrt(2*2 * 2*2) * sqrt(3)
2*2*sqrt(3)
4*sqrt(3)

now do sqrt(-1)* sqrt(-1)
use the rule that sqrt(x)*sqrt(x) = x

Answer 18

i m not telling him to memorize if u knows abt iota then he must be knowing about factoization of a number too...

Answer 19

yes i just learned that. didnt think that was involvd in this. sorry thought about if afterwards

Answer 20

sorry I am writing this down so i can have an example of what to do

Answer 21

now do sqrt(-1)* sqrt(-1)
use the rule that sqrt(x)*sqrt(x) = x

Answer 22

not sure what yor are saying sorry this is all new work for me.

Answer 23

there is rule (or definition) that says
sqrt(x) * sqrt(x) = x

for example,
sqrt(4)*sqrt(4)= 4
2 * 2 = 4 it worked
sqrt(9)*sqrt(9)= 9
3 * 3 = 9 yes it works,
sqrt(-1)*sqrt(-1)= ?

Answer 24

=1

Answer 25

look at the rule more carefully

Answer 26

I thought that two negatives = a positive. so -1*-1 = 1 is that what you are looking for

Answer 27

yes, -1* -1= +1
but we are doing
sqrt(-1)*sqrt(-1)
and we have to use the rule
sqrt(x) * sqrt(x) = x

Answer 28

or are you looking for 12*4 sqrt 3
I think I am not understanding what you are saying

Answer 29

sorry i am not one to just get an answer i want to know how to do it

Answer 30

OK, we can go over the why in a minute, but first, let's get the answer to your question
we have
\[ 12\cdot 4\sqrt{3}\cdot \sqrt{-1}\cdot\sqrt{-1} \]

we can simplify the last part by using sqrt(x)*sqrt(x) = x
so what is
\[ \sqrt{-1}\cdot\sqrt{-1} = ?\]

Answer 31

ok
I am writing it down.

Answer 32

um I am guessing would it be i for the imaginary number

Answer 33

no, i is short hand for \( \sqrt{-1} \) to save typing the square root of -1 all the time.
there is only one way to know what
\[ \sqrt{-1}\cdot\sqrt{-1} = ? \]
is, and that is to use the rule that the square of a number times the square root of that number is the number itself.

Answer 34

*use the rule that the square *root* of a number times the square root of that number is the number itself.

Answer 35

4*3 = 12

Answer 36

?

Answer 37

I am lost sorry I am trying to figure out what you are asking

Answer 38

The square root of -1 is -1 and two negatives equal a positive so I am not sure what you are saying or asking for

Answer 39

you said: The square root of -1 is -1 NO! -1*-1 = +1. so -1 is not the root of -1

If we insist that there is a number that is the root of -1, what is it? we say
sqrt(-1) is the root of -1, and when we multiply sqrt(-1)*sqrt(-1) we get -1

If this sounds strange, it is. There is no real number that is the root of -1. So people decided to call this strange number i (sqrt(-1)). i*i (by definition)= -1

The very interesting thing is that when you do this, a lot of new math shows up that solves all kinds of problems that could not be solved before. So people got used to using i and imaginary numbers.

Answer 40

ok so sqrt(-1)*sqrt(-1)= -1

Answer 41

yes. and now you can simplify
\[ 12\cdot 4\sqrt{3}\cdot \sqrt{-1}\cdot\sqrt{-1} \]

Answer 42

so will it be 12*4sqrt3*-1 or 12*4sqrt3*i

Answer 43

it is the first
12*4*sqrt(3)*-1

but you can do better, right: -1*4*12*sqrt(3) (order can be changed when multiplying)
can you finish the multiplication?

Answer 44

-48sqrt3

Answer 45

yes. I hope that how you got the answer makes sense.

Answer 46

yes so would that be the full answer to my question at the top. because someone else sent x=sqrt-144 = +-12i. and I have no clue how they got that

Answer 47

\[ sqrt{-144} = \sqrt{144}\cdot\sqrt{-1}\]
now you should REMEMBER \(\sqrt{-1}=i\)
and \( \sqrt{144}= ±12 \)

Answer 48

*that first thing should be sqrt(-144)

Answer 49

they did not multiply by sqrt(-48) , probably because it is not clear in the question

Answer 50

oic ty soooooo much for being patient and showing me how as well as explaining to me how to do it. Is there anything that I can do for you to show that i am appreciated ,with your help?

Answer 51

just keep up the good work!
btw, wolfram can do these things, so you can check your answers.
for example, see
http://www.wolframalpha.com/input/?i=sqrt%28-144%29*sqrt%28-48%29