Help on simplifying rational expresssion sqrt of 5x square -

[googleplex]

I don't know where to begin with the following problem:

simplify the square root of 5x square -10x + 5.

The directions say to find a simplified form of f(x) while assuming x can be any real number. Do I factor out the largest common factor or what?

 

[Denis]

Re: Help on simplifying rational expresssion

Start by dividing by 5.

 

[stapel]

I don't know where to begin with the following problem:

simplify the square root of 5x square -10x + 5.

A good start would be to clearly state what the expression is. As currently formatted, your meaning is unclear.

I will guess that you probably mean "sqrt[5x^2 - 10x + 5]", or:

. . . . .\(\displaystyle \sqrt{5x^2\, -\, 10x\, +\, 5}\)

If so, then a good first step would be the one suggested in the previous reply: take out the common factor of 5:

. . . . .\(\displaystyle \sqrt{5\left(x^2\, -\, 2x\, +\, 1\right)}\)

The remaining quadratic factors. In fact, it is a "perfect square". So put the quadratic into perfect-square form (namely, (x - a)[sup:3uzr6gw9]2[/sup:3uzr6gw9]), and take the square root. Your answer should look something like:

. . . . .\(\displaystyle \sqrt{5}\left(x\, -\, a\right)\)

...where you've replaced "a" with the value you found when you factored.

If you get stuck, please reply showing all of your work and reasoning so far. Thank you!