Question

need help simplifying \[x \sqrt{3} +3x \sqrt{3} + \sqrt{27x^2}\]

Answer 1

\[\Large\bf\sf \color{royalblue}{\left(x \sqrt3\right)}+3\color{royalblue}{\left(x \sqrt3\right)}+\sqrt{27x^2}\]

\[\Large\bf\sf \color{royalblue}{\left(apple\right)}+3\color{royalblue}{\left(apples\right)}+\sqrt{27x^2}\]

Answer 2

The first two terms can be combined.

Answer 3

you can simply the sqrt(27x^2) as well

Answer 4

simplify* , the sleepiness is getting to me D:

Answer 5

\[\Large\bf\sf =4\color{royalblue}{\left(apples\right)}+\sqrt{27x^2}\quad=\quad 4\color{royalblue}{\left(x \sqrt 3\right)}+\sqrt{27x^2}\]Understand what I did there ?:o

Answer 6

@zepdrix yes thank you very much

Answer 7

The last term can be simplified also, as sham mentioned.
I'm just a little bit concerned because it seems like we should be getting |x|, not x...
But uhhhh... let's not worry about that I guess.\[\Large\bf\sf \sqrt{27x^2}\quad=\quad \sqrt{(9x^2)\cdot 3}\quad=\quad (3x)\sqrt{3}\]

Answer 8

@zepdrix if you are simplifying a number with an exponent to a power you just cut the power in half and move it to the front of the square root symbol?

Answer 9

For `square roots`, yes.
That's a good way to interpret it.

Answer 10

@zepdrix for example if it is \[\sqrt{72x^9}\] I would just say that is \[6x^3\sqrt{2}\]?

Answer 11

You would want to separate what can be pulled out of the root and what can't.\[\Large\bf\sf \sqrt{72x^9}\quad=\quad \sqrt{36x^8\cdot 2x}\quad=\quad \sqrt{\color{royalblue}{6^2x^8}\cdot 2x}\]The blue part is what we're able to cut in half evenly.\[\Large\bf\sf =\quad 6x^4 \sqrt{2x}\]

Answer 12

In your example, you didn't properly cut the 9 in half.

Answer 13

Unless you had meant to type 6 for the exponent :) heh

Answer 14

oooh okay thank you very much

Answer 15

to be picky, you can't do all of that simplification unless you know that \(x>0\)