Question

Evaluate -9^(1/2)

Answer 1

the one half in the exponent means take the square root

Answer 2

The answer in the back says it's -5. I don't understand how to get that. So it would be\[\sqrt{-9}\]

Answer 3

\(-5\) is not possible,. perhaps you are looking at the wrong numbered problem
in any case it is not \[\sqrt{-9}\] but rather \[-\sqrt9\] the minus sign is out fron

Answer 4

My bad, it's -3 in the book.

Answer 5

yes that is right

Answer 6

Wouldn't it be a +/- 3i or something?

Answer 7

no it would not
lets look at a simpler example

Answer 8

what is \[100-5^2\]?

Answer 9

75?

Answer 10

yes because \[100-5^2=100-25=75\]

Answer 11

now what is \[-5^2\]?

Answer 12

-25

Answer 13

right

Answer 14

notice that the minus sign stays right out front, since what is beings squared is \(5\) not \(-5\)

Answer 15

now consider \[-9^{\frac{1}{2}}\] what are you taking the square root of?

Answer 16

-9

Answer 17

Oh wait, 9?

Answer 18

right

Answer 19

So the square root of 9 is three and then you add the - sign so it's -3?

Answer 20

just like \[-5^2=-5\times 5=-25\] the exponent is for the \(5\) not \(-5\)

Answer 21

yes exactly
the square root of nine is three and the minus sign stays there

Answer 22

Okay, I think I get it now. Thank you!

Answer 23

yw