Simplifying radicals

[skaterchicky23]

Hello,

I have an equation of

12x^5y^3(a+b)^2 -The whole equation is under a square root sign, but I was unsure of how to write that on this forum
--------------------
5z

I need to simplify this equation

I started by doing

12x^5y^3(a+b)(a+b) I put a square root over the numbers in the numerator and a separate square root in the
----------------------- denominator
5z

12x^5y^3(a^2-2ab+b^2)
____________________ The numerator has a separate square root and the denominator has a separate square root
5z


The last step I have is

3*2*2x^5y^3a^2+2*2*2*3x^5y^3ab+3*2*2x^5y^3b^2
___________________________________________
5z

Both still have the same square root signs as above
This is the final step I have, I'm not sure where to go from here, or if this is even correct

please help

 

[Loren]

Step 1. Look up the definition of "equation".

Step 2. Look up the definition of "expression".

Step 3. Rephrase your question.

 

[skaterchicky23]

Hello,

I have an expression of

12x^5y^3(a+b)^2 -The whole expression is under a square root sign, but I was unsure of how to write that on this
-------------------- forum
5z

I need to simplify this expression

I started by doing

12x^5y^3(a+b)(a+b) I put a square root over the numbers in the numerator and a separate square root in the
----------------------- denominator
5z

12x^5y^3(a^2-2ab+b^2)
____________________ The numerator has a separate square root and the denominator has a separate square root
5z


The last step I have is

3*2*2x^5y^3a^2+2*2*2*3x^5y^3ab+3*2*2x^5y^3b^2
___________________________________________
5z

Both still have the same square root signs as above
This is the final step I have, I'm not sure where to go from here, or if this is even correct

please help

 

[Loren]

There are many different approaches to the simplifying radicals. I'll start by reminding you that...
\(\displaystyle \sqrt{a^2}=\pm a\) and \(\displaystyle \sqrt{a^3}=\sqrt{a^2\cdot a}=a\sqrt{a}\)
Another rule we will use is...
\(\displaystyle \sqrt{a}\cdot \sqrt{a}=a\)
Finally,...
\(\displaystyle 1=\frac{\sqrt{a}}{\sqrt{a}}\)
\(\displaystyle \frac{\sqrt{12x^5y^3(a+b)^2}}{\sqrt{5z}}\)
One approach is to rewrite in this fashion. You figure out why.

\(\displaystyle \frac{\sqrt{2^2\cdot 3 \cdot x^4\cdot x\cdot y^2\cdot y\cdot (a+b)^2}}{\sqrt{5z}}\)

This allows you to quickly determine which factors can be removed from under the radical sign. I'll "bring out" two of them. You can bring out the rest.

\(\displaystyle \frac{2x^2\sqrt{3\cdot x\cdot y^2\cdot y\cdot (a+b)^2}}{\sqrt{5z}}\)

After bringing out the rest, you might multiply both numerator and denominator by the denominator. This will give you 5z in the denominator and a 5z will be an additional factor under the radical sign in the numerator. I am saying this on the assumption that part of the "simplification" process involves not ending up with a radical in the denominator. I'm going to go ahead and give you my final answer. I know that you will have many more problems of like nature that you will have to do on your own. Please, don't let me down. Figure out why we have done what we have done.
\(\displaystyle \frac{2x^2y(a+b)\sqrt{15xyz}}{5z}\)

 

[stapel]

The whole expression is under a square root sign, but I was unsure of how to write that on this forum

For formatting information, try following the advice in the two articles in the links you saw in the "Read Before Posting!" thread you read.

Eliz.