Question

directions are simplify each radical if possible if imaginary rewrite in terms of i and simplify? Then it has the square root of -16

Answer 1

Your question is not clear.

Answer 2

the answer comes out to 4i so if you have the square root of 27 what would you get

Answer 3

\[\sqrt{-16} = \sqrt{16} \sqrt{-1} = 4i\]

Answer 4

\[\sqrt{27} = \sqrt{3^2 \cdot 3} = 3 \sqrt3\]

Answer 5

now the square root of 72 and how do you know what numbers to use King George you are doing great!

Answer 6

??

Answer 7

The key to doing this is to completely factor the radicand. So 72 in this case. To completely factor 72, we first divide by 2, so we have \[72 = 2 \times 36\] We then repeat this process until we it is no longer divisible by 2. \[72 = 2 \times 36 = 2 \times 2 \times 18 = 2 \times 2 \times 2 \times 9 = 2^3 \times 9\] Now we factor 9, so \[72 = 2^3 \times 9 = 2^3 \times 3 \times 3 = 2^3 \times 3^2\] Then we can easily take the square root of this. \[\sqrt{72} = \sqrt{2^3 \times 3^2} = \sqrt{2 \times (2^2 \times 3^2)} = \sqrt2 \times (2 \times 3) = 6\sqrt2\]

Answer 8

If you take the square root of some number with an even exponent, simply divide the exponents by two.

Answer 9

thank you so much!! You have been a big help!

Answer 10

no problem whatsoever.

Answer 11

what about a square root of -45/36

Answer 12

these are hard

Answer 13

\[\sqrt{-{{45} \over {36}}} = {\sqrt{-45} \over \sqrt{36}} = {3i \sqrt5 \over 6} = {i \sqrt5 \over 2}\] I'm skipping some of the steps I've told you about just before, but we know that the root of 36 is 6, and 45 is 5 times 9

Answer 14

wow thanks again!!!!!!!

Answer 15

you're very welcome

Answer 16

I hope I can find you on more often!!!

Answer 17

I'm on every now and then. I'm making an effort to be here more often this semester.

Answer 18

good because a lot of people could benefit from your help! you should be a paid tutor

Answer 19

I might. If I have to get another job, I'll definitely consider it.

Answer 20

how about -49/75

Answer 21

I know how to do the first step of putting the square root of -49 /square root of 75 but what then

Answer 22

I dont understand the i part

Answer 23

well if you factor 49, you get 7 x 7. So \[-49 = {-1} \times 7^2\] so the square root of the whole thing is just\[\sqrt{-49} = 7\sqrt{-1}\] This is where the i comes in. Since \[i = \sqrt{-1}\]\[\sqrt{-49} = 7\sqrt{-1} = 7i\] That's really all i is. It's a pretty simple concept once you understand it.

Answer 24

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Answer 25

so what is the answer for that problem then

Answer 26

since \[\sqrt{-49} = 7i\]and\[\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt3\]\[\sqrt{-49 \over 75} = {7i \over 5\sqrt3} = {7i \sqrt3 \over 15}\]That last step you can get by multiplying by \[\sqrt3 \over \sqrt3\]

Answer 27

I'll be back in a few minutes if you still have more questions.

Answer 28

ok thank you

Answer 29

That is all for tonight so thank you so much!!! You ought to be a paid helper! Check into that posting I sent you it came up on my screen so you should really do it!