how would u simplify this radical form?
sqrt{45x^2}

Question

how would u simplify this radical form?
sqrt{45x^2}

campbell_st · Answer

$$\sqrt{45x^2} = \sqrt{9 \times 5 \times x^2 } = \sqrt{9} \times \sqrt{x^2} \times \sqrt{5}$$

you can find the square root of 9 and x^2    

so the answer is 

$$3x \sqrt{?}$$

anonymous · Answer

good ths wt i did

chriss · Answer

So you would want to start by breaking this up as much as possible... I'd start by separating the coefficient from the variable

$$\sqrt{45x^{2}}=\sqrt{45}\sqrt{x^{2}}$$

Now 45 isn't a perfect square, but it can be factored and one of it's factors is a perfect square.  Also the square root of x^2 is x.
$$x*\sqrt{45}=x*\sqrt{9}\sqrt{5}$$
and 9 is a perfect square so you can simplify that further and you will get
$$3x \sqrt{5}$$

anonymous · Answer

That is usually the way it is done, but technically, $$\sqrt{x^2}=|x|$$which may make the desired answer $$3\sqrt{5}|x|$$

chriss · Answer

In general
$$\sqrt{x}$$
is accepted to mean the positive square root of x.

anonymous · Answer

That's exactly the convention, and that's also the reason that the square root of x^2 is the absolute value of x.  If x is negative, the square root of its square is its opposite.

chriss · Answer

I gotcha.  Which is why then the answer as you described it would be the absolute value of x as opposed to + or - x.