Question

solve equation by square root property

r(2sq) + 36 = 0

Answer 1

@jim_thompson5910

Answer 2

@XxNina26xX

Answer 3

@perl

Answer 4

it's written as r to the second power

Answer 5

Hint:

r^2 + 36 = 0

turns into

r^2 = -36

Answer 6

0?

Answer 7

no

Answer 8

oh wait, -6

Answer 9

-18? sorry i'm graduating in a week from high school, i just need to finish this and i'm done but i need help :(

Answer 10

have you learned about imaginary numbers? or complex numbers?

Answer 11

no

Answer 12

well congratulation. But guessing isn't going to get you to graduation.

Answer 13

i don't mean to guess, then help me please! lol

Answer 14

do you understand square root property?

Answer 15

if you start with r^2 and you replace r with -6, what do you get?

Answer 16

yea

Answer 17

-36!

Answer 18

no

Answer 19

- x - ?

Answer 20

36

Answer 21

r^2 = (-6)^2

(-6)^2 = (-6)*(-6)

(-6)^2 = 36 ... notice how it's positive

Answer 22

better

Answer 23

you can take any number that's not 0 and square it

it will always be positive

Answer 24

so what this means is that r^2 = -36 has no real solutions

but it does have solutions...they're just not considered real numbers

Answer 25

oh so it would be -6?

Answer 26

the convention is to make the letter i be equal to sqrt(-1)

so

i = sqrt(-1)

notice how if you square both sides, you'll get

i^2 = -1

Answer 27

i = sqrt(-1) is known as an imaginary number

Answer 28

okay :)

Answer 29

technically all numbers are imaginary since we made them all up, so it's not really fair to call i = sqrt(-1) an imanigary number...but that's just how history played out

Answer 30

imaginary*

Answer 31

oh lol so i got 6 for r cause 6x 6 is 36

Answer 32

anyways,

i = sqrt(-1)

so we'll use this to solve for r

r^2 = -36

r = sqrt(-36)

r = ??? ... how will we use the first equation above to simplify?

Answer 33

6 is close...but not the full story

Answer 34

6 x -1?

Answer 35

I'll give you a further hint (if you're still stuck)

r = sqrt(-36)

r = sqrt(-1)*sqrt(36)

r = ???

Answer 36

and remember that i = sqrt(-1)

Answer 37

-6

Answer 38

sqrt(36) = ???

Answer 39

so 36 x 36?

Answer 40

i want you to start with

r = sqrt(-1)*sqrt(36)

Answer 41

and replace sqrt(-1) with ???

and also replace sqrt(36) with ???

Answer 42

2

Answer 43

what did we make sqrt(-1) equal to

Answer 44

i?

Answer 45

yep

Answer 46

what is sqrt(36) equal to

Answer 47

6?

Answer 48

so

r = sqrt(-1)*sqrt(36)

turns into

r = i*6

which flips to

r = 6i

Answer 49

why i?

Answer 50

because i = sqrt(-1)

Answer 51

notice how we just replaced sqrt(-1) with i

Answer 52

but is i r?

Answer 53

no i is its own thing

Answer 54

oh.. okay thanks! here's another one

Answer 55

wait, it turns out that -6i works as well (in much in the same way -6 works for r^2 = 36)

Answer 56

so the two solutions to

r^2 + 36 = 0

are

r = 6i
r = -6i