Simplifying radical expressions: SQRT81x^12y^8z^10

[flora33]

Ok, I'm not quite sure if I'm grasping these. Please take a look and let me know where I'm going wrong. Since I don't know code, I'm going to put SQRT in place of the radical symbol.

Simplify the expression:

SQRT81x^12y^8z^10
SQRT27x^9y^6z^9 * SQRT3x^36^2z
3x^3y^2z^3 SQRT3x^3y^2z

Thanks!

Flora

 

[Deleted member 4993]

Re: Simplifying radical expressions

Ok, I'm not quite sure if I'm grasping these. Please take a look and let me know where I'm going wrong. Since I don't know code, I'm going to put SQRT in place of the radical symbol.

Simplify the expression:

SQRT81x^12y^8z^10

=SQRT81 * sqrt(x^12) * sqrt(y^8) * sqrt(z^10)

= 9 * x^6 * y^4 * z^5

SQRT27x^9y^6z^9 * SQRT3x^36^2z <<< I don't understand why are you doing this step. If the question was to take "cube-root" - this would make sense.
3x^3y^2z^3 SQRT3x^3y^2z<<< You have taken "cube-root" of the first factor

Thanks!

Flora

 

[flora33]

Re: Simplifying radical expressions

...I'm going to put SQRT in place of the radical symbol.

Simplify the expression: SQRT81x^12y^8z^10

=SQRT81 * sqrt(x^12) * sqrt(y^8) * sqrt(z^10)

= 9 * x^6 * y^4 * z^5

SQRT27x^9y^6z^9 * SQRT3x^36^2z <<< I don't understand why are you doing this step. If the question was to take "cube-root" - this would make sense. I'm not sure either.
3x^3y^2z^3 SQRT3x^3y^2z<<< You have taken "cube-root" of the first factor

I tried to do it like this the first time:
SQRT(9*9*x*x*x*x*x*x*x*x*x*x*x*x*y*y*y*y*y*y*y*y*z*z*z*z*z*z*z*z*z*z) I found this method on purplemath.com because my book doesn't seem to explain how to do these very well. Is there a different way to approach this? Obviously the method I was trying is wrong!
Then I took out all of the factors occuring in pairs and arrived at your answer: = 9 * x^6 * y^4 * z^5
I should have stuck with that. I'm slowly getting there with radical expressions. They are pretty beyond me!

Thanks for your help!
Flora

 

[stapel]

Is there a different way to approach this? Obviously the method I was trying is wrong!

The question wasn't with respect to your "approach" or "method". You stated that the expression involved a SQUARE root, but then you simplified as though it were a CUBE root. Which is it? (Until we know what the question was, I'm afraid it is unlikely that we will be able to determine the validity of your answer. Sorry!)

Please reply with the requested information. Thank you!

Eliz.

 

[flora33]

Re:

You stated that the expression involved a SQUARE root, but then you simplified as though it were a CUBE root. Which is it? (Until we know what the question was, I'm afraid it is unlikely that we will be able to determine the validity of your answer. Sorry!)

Please reply with the requested information.

Well, I don't think it was supposed to be simplified as though it were a cube root. It is supposed to be simplified... and I was not aware there was a difference of simplifying it as a square root or cube root. I follow the instructions provided by my book, that's all. In this case, as noted earlier, I went to purplemath.com and used that method because my book doesn't provide enough of an explanation as to how to work this problem out. My instructor makes himself available one hour a week- so as a result I'm left to figure this stuff out on my own. Math is not my strong point, so this class has been a struggle every single week. I hope I answered your question. Sorry about the vent, I am just really frustrated in general and I can't wait for this class to be over.

Flora

 

[Mrspi]

Re: Re:

I was not aware there was a difference of simplifying it as a square root or cube root....

If you are not clear that there is a BIG difference between a square root and a cube root, then I'd make SURE to bring this up with your instructor!

The square root of a number is what you use as a factor TWO TIMES to get that number. For example, x*x = x^2, so sqrt(x^2) = x. 5*5 = 25, so sqrt(25) = 5.

The cube root of a number is what you use as a factor THREE TIMES to get that number. Since n*n*n = n^3, cubrt(n^3) = n. And since (-2)*(-2)*(-2) = -8, cubrt(-8) = -2.

Suppose you have to find sqrt(x^10)....from the rules of exponents, you should realize that x^10 is the same thing as x^5*x^5. So, sqrt(x^10) = x^5.

Suppose you have to find cubrt(x^12)....again, from the rules of exponents you should realize that x^12 is the same thing as x^4 * x^4 * x^4. So, cubrt(x^12) = x^4

Once you have learned about fractional exponents (and I don't know if you've done this yet), things are a bit easier. sqrt(n) can be written as n^(1/2) If you are asked to find sqrt(x^10), you can write that as (x^10)^(1/2). NOW, use one of the rules of exponents which says that when you raise a power to a power, you MULTIPLY the exponents. So,

(x^10)^(1/2) = x^(10*(1/2))
or,
x^5

And cubrt(n) = n^(1/3)
So, if you're looking for cubrt(x^12), you can write that as (x^12)^(1/3)
Or, x^(12*(1/3))
or, x^4

See...same answers, but a bit of a different way of looking at it.

 

[flora33]

Re: Re:

I was not aware there was a difference of simplifying it as a square root or cube root....

If you are not clear that there is a BIG difference between a square root and a cube root, then I'd make SURE to bring this up with your instructor!

The square root of a number is what you use as a factor TWO TIMES to get that number. For example, x*x = x^2, so sqrt(x^2) = x. 5*5 = 25, so sqrt(25) = 5.

The cube root of a number is what you use as a factor THREE TIMES to get that number. Since n*n*n = n^3, cubrt(n^3) = n. And since (-2)*(-2)*(-2) = -8, cubrt(-8) = -2.

Suppose you have to find sqrt(x^10)....from the rules of exponents, you should realize that x^10 is the same thing as x^5*x^5. So, sqrt(x^10) = x^5.

Suppose you have to find cubrt(x^12)....again, from the rules of exponents you should realize that x^12 is the same thing as x^4 * x^4 * x^4. So, cubrt(x^12) = x^4

Once you have learned about fractional exponents (and I don't know if you've done this yet), things are a bit easier. sqrt(n) can be written as n^(1/2) If you are asked to find sqrt(x^10), you can write that as (x^10)^(1/2). NOW, use one of the rules of exponents which says that when you raise a power to a power, you MULTIPLY the exponents. So,

(x^10)^(1/2) = x^(10*(1/2))
or,
x^5

And cubrt(n) = n^(1/3)
So, if you're looking for cubrt(x^12), you can write that as (x^12)^(1/3)
Or, x^(12*(1/3))
or, x^4

See...same answers, but a bit of a different way of looking at it.

Well, I do know there is a big difference between a square root and a cube root but on this particular problem my teacher gave us, he did not say whether it is to be simplified as either one. I assume it is supposed to be simplified as a square root because it does not have the index 3.... So, I suppose I just performed the calculations wrong and need to spend more time hunting for other resources other then my text, because it is not a good resource. Thanks for the info.

Flora