# Thread: Simplify expression - steps?

1. ## Simplify expression - steps?

THe link below shows a picture of a problem i need help in how can i solve it? what are the step by step? you can also help me solve it so i can find ot how to solve my other problems. Thanks ;]

http://img369.imageshack.us/my.php?image=dsdsdsyw2.png

2. do you know the rule for manipulating radicals
$\displaystyle \sqrt{ab}=\sqrt{a} \times \sqrt{b}$

so use this and taking out the common factor of $\displaystyle \sqrt{x^2}=|x|$

then use the fact that $\displaystyle \sqrt{90}=\sqrt{9} \times \sqrt{10}=3 \sqrt{10}$

3. i still don't know how should i do the problem.... is there a step by step showing of that problem. im sorry. ;[

4. We start with: $\displaystyle 5\sqrt{10x^2} - \sqrt{90x^2}$

We can simplify the second radical by pulling out a factor of 9: $\displaystyle 5\sqrt{10x^2} - \sqrt{9} \cdot \sqrt{10x^2}$

Then the square root of 9 becomes 3: $\displaystyle 5\sqrt{10x^2} - 3\sqrt{10x^2}$

We combine the like terms: $\displaystyle 2\sqrt{10x^2}$

We can also take out a factor of x^2: $\displaystyle 2\sqrt{x^2} \cdot \sqrt{10}$

The square root of x^2 is the absolute value of x: $\displaystyle 2|x|\sqrt{10}$

And the problem is done, because $\displaystyle \sqrt{10}$ cannot be further broken down.