Question

Square Root Problem. Need help. See comments

Answer 1

\[\sqrt{216p^3q ^{12}}\]

Answer 2

Well that just looks amazing doesn't it? :)

Answer 3

I dont understand why in the answer sometimes the root has an index when we started with just a square root. And yes this is nicer then some of the ones I have lol

Answer 4

OK, well we'll take a look at the whole index issue soon enough I'm sure. How would you think to start on this one?

Answer 5

Well I know that 216 is 6x36
p^3= p x p^2
q^12= q^4 x q^3

Answer 6

\[\sqrt{216p^3q^{12}}=\sqrt{6^2.6.p^2.p.q^{12}}=6pq^6\sqrt{6p}\]

Answer 7

why are we keeping q^12?

Answer 8

We don't have to it just so happens that q^12 = (q^6)^2 so that the square root cancels it nicely. Otherwise you could write:

q^12 = q^2 * q^2 * q^2 * q^2 * q^2 * q^2

Then, take the square root and get

q*q*q*q*q*q = q^6 as before.

Answer 9

oh. that makes sense.

Answer 10

I like to think of the square root as sort of a "exponent-halving" machine. It takes the power as halves it.

Answer 11

In this case, I would personally think that @anupsunni has the fully reduced answer. Does that match up with the answer the problem wanted?

Answer 12

yes it did. other then it should be the absolute value of p on the outside.

Answer 13

Ah... indeed, that is true. :) Just because p^2 = 4 for example, we don't know that p has to equal 2 it could be -2, so the safest answer is |p|

Answer 14

so if I have \[\sqrt{32y^4}\] this would simplify to \[4y^2\sqrt{2}\]

Answer 15

yes that is it!

Answer 16

In this case, no absolute value bars are necessary since we still have y^2 which takes care of any negative vs. positive problems.

Answer 17

right. just like with y^3 theres no restrictions

Answer 18

Part of me thinks that you could actually argue that it should be |y^3| because cubing a number does not guarantee a positive answer. For example (-2)*(-2)*(-2) = -8 vs. (2)*(2)*(2) = +8.

Answer 19

yeah thats right. I meant the cube root and negatives.. im sorry. Im trying not to freak out over this huge test on Wednesday.

Answer 20

No worries. I see what you mean. You've got time. :)

Answer 21

Now, about your index question are you referring to symbols that look like this?
\[\sqrt[3]{x^2}\]

Answer 22

\[\sqrt{27p^3q ^{10}}\]

Answer 23

the answer to this the index changed

Answer 24

Hmm... that seems odd... I'm not sure I would trust that answer.