SOLUTION: simplify root symbol 39a^3b^5/root symbol 13a2b I am having difficulty with this can you help please????

Question 623092: simplify
root symbol 39a^3b^5/root symbol 13a2b
I am having difficulty with this can you help please????
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I assume by "root symbol" you mean square root. (In the future, please specify which kind of root.) I also assume that "13a2b" means

There are several ways to deal with a fraction of square roots. My prefernce is to do the following:

Use the property to join the two square roots into one.
Reduce the fraction. (Note: If you're clever you will keep in mind step 3 and maybe not reduce the fraction as fully as possible. For example, if you had then you would not reduce the fraction because step 3 wants perfect square denominators. 4 is already a perfect square. If we reduce 2/4 to 1/2 then we would no longer have a perfect square denominator. And we would end up changing 1/2 back to 2/4 in step 3.)
If there still is a denominator, then make sure it is a perfect square.
If there still is a denominator, then use the property again, this time in the other direction -- to split the numerator from the denominator.
Simplify any remaining square roots and fractions.

Let's see this in action:

1. Join the square roots:

2. Reduce the fraction (maybe not fully).
The entire denominator cancels out leaving:

or just

3. If there's a still denominator, ...
There is no denominator.
4. If there's a still denominator, ...
There is no denominator.
5. Simplify any remaining square roots and fractions.
To simplify a square root, look for perfect square factors of the radicand (the expression inside). There are not prefect square factors in the 3 or the a. But there are perfect square factors in . When I factor out the perfect squares I like to put those factors in front:

Then you use another property of radicals, , split the square root so that eah perfect square factor is in its own square root:

The square roots of the perfect squares simplify:

which simplifies to:

RELATED QUESTIONS
Now I am lost...please help me. Simplify by combining like terms: 63 square root... (answered by elima)

I am having a lot of difficulty with this problem. I hope the modified square root... (answered by stanbon)

HELP! I am new at this square root thing. I am not sure how I enter the 'square root'... (answered by josmiceli)

Hello, this question isn't from a book. It is a paper assignment. Please help I am... (answered by 303795)

Can you help with this Algebra I practice test problem? Write a quotient without a... (answered by nerdybill)

Having problems with square root equations; for example, 5{square root symbol}27 -... (answered by checkley71)

I don't know if I wrote this problem correct, but here goes: Simplify the cube root. 3... (answered by jim_thompson5910)

I'm having problems figuring this problem out. Can someone help me on this one? The... (answered by ankor@dixie-net.com)

Please help me simplify this expression. (3-2√7) (3+2√7) FYI- The symbol (answered by stanbon)