Question

Indicate whether the conjecture is true or false. If false, provide a counterexample.

Answer 1

do you think it's true or false?

Answer 2

I'm not sure how to find out.

Answer 3

if you square a positive number, then take the square root of that result, what do you get?

Answer 4

so like 5 squared = 25 so the square root is 5

Answer 5

how about squaring 7 and then taking the square root of that

Answer 6

it equals 7

Answer 7

so it would be true right?

Answer 8

so for any positive number, squaring it, then taking the square root gives you the same number

Answer 9

what happens when you start with a negative number?

Answer 10

it comes out negative

Answer 11

no wait....i dont think a negative can have a squareroot right?

Answer 12

say you start with -10

square -10 to get ???

Answer 13

3.16?

Answer 14

square, as in multiply it by itself

Answer 15

opps sorry...it would be -100

Answer 16

no, -10 squared = (-10) * (-10) = ???

Answer 17

when we have x^2 and we replace x with -10, then we square all of -10

Answer 18

x^2 = (-10)^2 = (-10)*(-10) = ???

Answer 19

im getting confused i swear i squared -10 right...

Answer 20

nope i guess i didn't sorry it would turn out a positve 100 not neg.

Answer 21

now take the square root of 100 to get ?

Answer 22

10

Answer 23

so is \[\Large \sqrt{x^2} = x\] true when x is a negative number?

Answer 24

no

Answer 25

good, the left side is always positive, while the right side of just x is negative (when x is negative)

Answer 26

to fix this, we replace x on the right side with |x|

Answer 27

so \[\Large \sqrt{x^2} = |x|\] is definitely true for all real numbers