Question

What is the square root of -25?

Answer 1

I need the imaginary number

Answer 2

-[5] maybe

Answer 3

i5

Answer 4

that is the square root since i=square root -1

Answer 5

Okay so it would be -5, but then the i makes it positive?

Answer 6

sqrt 25 = 5, sqrt -1 = i

Answer 7

no its i5

Answer 8

u are right

Answer 9

its usually written 5i

Answer 10

okay thanks

Answer 11

it doesn't matter either way

Answer 12

I want to give you all medals :(

Answer 13

i is short for \( \sqrt{-1} \)
and the idea is
\[ \sqrt{-1} \sqrt{-1} = -1 \]
notice
5i means 5*i
and
\[ (5i)^2 = 5 \cdot i \cdot 5 \cdot i = 5 \cdot 5 \cdot \sqrt{-1}\cdot \sqrt{-1} \\=25\cdot -1 = -25
\]

Answer 14

Okay, that makes sence to me

Answer 15

but I also have \[3\sqrt{-49}\]

Answer 16

people sometimes think -5 is the square root of -25
but -5*-5 = + 25
so we need to use i

for square roots, always break it into -1 and then the positive number
so -49 = -1 * 7*7
now you can do the square root of that

Answer 17

And thats also were I get stuck, I have the others once it was just those too

Answer 18

\[ \sqrt{-1 \cdot 7 \cdot 7}= \sqrt{-1} \cdot \sqrt{7\cdot 7} \]

Answer 19

I assume you know how to "take out a pair" from the square root?
for example, \( \sqrt{7\cdot7}= 7 \)

Answer 20

Yes, I think so

Answer 21

and any time you see \( \sqrt{-1}\) remember to use its "nickname" i

Answer 22

okay, I never put realized it was the same, it makes so much seance now

Answer 23

sense

Answer 24

what do you get for
\[ 3 \sqrt{-49} \]?
remember the 3 "out front' means 3 times sqr(-49)

Answer 25

Right so 16.3?

Answer 26

how did you get that ?

Answer 27

division?

Answer 28

let's just look at
\[ \sqrt{-49}\]
do you now we can write -49 as -1 * 7 * 7 ?

Answer 29

it doesnt work

Answer 30

Wait....

Answer 31

yes it does lol

Answer 32

the idea of a square root is you can write
\[ \sqrt{7 \cdot 7}= 7 \]

Answer 33

do I need to simplify that?

Answer 34

so with -49 write it as -1*7*7
now do the square root
\[ \sqrt{-49}= \sqrt{-1 \cdot 7 \cdot 7} \]
remember we can write this as
\[ \sqrt{-1 \cdot 7 \cdot 7} = \sqrt{-1} \cdot \sqrt{ 7 \cdot 7}\]

Answer 35

you should be able to simplify this now:
\[ \sqrt{-1} \cdot \sqrt{ 7 \cdot 7}\]

Answer 36

what letter should you use to replace the \( \sqrt{-1} \) ?
and how do you simplify \( \sqrt{7 \cdot 7} \) ?
(see up above)

Answer 37

So it would be just 49?

Answer 38

7*7 is 49
\( \sqrt{7\cdot 7} \text{ is } 7 \)

Answer 39

Or if you are confused, you could use a calculator to find sqr(49)
though it would be better if you can do this problem in your head: 7*7 is 49
and sqr(7*7) is7

Answer 40

yup, thanks

Answer 41

i gtg but thank you!!!!

Answer 42

The answer is 5i.