Question

Help with this?

Answer 1

Remember that \(\sqrt{x^2} = x\), and that \(\sqrt{abc} = \sqrt{a} \sqrt{b} \sqrt{c}\).

Answer 2

Post what you think the next step is. See attachment.

Answer 3

@Directrix I really would suggest using LaTeX. :)

Answer 4

It's no good. \(\sqrt{x^{2}} = |x|\), but \(\sqrt{x}\cdot\sqrt{x} = x\). Not quite the same thing.

Answer 5

I appreciate your caring enough about my work to make a suggestion. I don't care for LaTex, MathJax, and whatever else pops up here on OS because the function of these programs is, for my computer, intermittent. When the aforementioned programs attempt to load on my computer, the entire browser minimizes and a snapping sound emits from my computer speakers. Much of the time, my machine cannot read the LaTex posted on the site.

And, I don't care to change browsers or to make other adjustments because my computer functions well on all other sites.

I do appreciate the suggestion and will keep it in mind. One day, I may surprise you with a LaTex post. Thanks.

Answer 6

@Directrix The reason I suggested LaTeX is because hand-drawn images are hard to read.
Also, it's your choice, ultimately if you're helping, who cares what method you use (of course, no dirty tricks like telling answers) :)

Answer 7

Personal Endorsement: From my point of view, a valuable asset like Directrix can use crayons if so desired. :-)

Answer 8

@tkhunny You know me too well. I do like crayons and colored pencils. Because I especially like Geometry problems, I find the different color options on Word and the snipping tool to be invaluable. Then, there's the drawing and marking up of the Geometry diagrams. I just like it. And, as you mentioned, there are inherent problems with LaTex or any computer program for that matter.

Answer 9

Ugh I have no clue. :(

Answer 10

You are not allowed to have "no clue". I simply do not believe it.

\(\sqrt{50} = \sqrt{25\cdot 2} = \sqrt{25}\cdot \sqrt{2} = \sqrt{5^{2}}\cdot \sqrt{2} = 5\cdot\sqrt{2}\)

That is the hard piece. You do the variables.

Answer 11

@tkhunny

If I were given the following question along with the instruction to determine if the statement were true or false, here's what I would write.

√(x*x) = √x * √ x = x. ----> FALSE

Counterexample:

√[(-2)*(-2)] = √(-2) * √(-2) = -2 which is not true.

Answer 12

@Directrix

I wrote two entirely separate statements.

\(\sqrt{x^{2}} = |x|\)

and

\(\sqrt{x}\cdot \sqrt{x} = x\)

The first requires no assumption or Domain restriction in the Real Numbers.
The second requires \(x \ge 0\)

At no time did I suggest any equality for the two statements.