Question

Need help with radicals!
Assuming x > 0, what is the simplified fraction form for 15x√3 / √75x^2 <--all under radiacal

I have to type the answer into a box and before it, its says:
Numerical Answers Expected!

After I multiplied the bottom radical by the top and bottom, I had:
15x√3 * √75x = 15√225x^3
√75x^2 * √75x^2 = 775x^2

Now I have: 15x√225x^3 / 75x^2
Simplified: 225x^2√x / 75x^2

Now I'm not sure where to go from here!

Answer 1

is the original question, \(\large \dfrac{15x\sqrt3}{\sqrt{75x^2}}\)
?

Answer 2

yes, that's how it's supposed to be

Answer 3

ok, there was no need to multiply and divide by \sqrt 75 x or \sqrt 75x^2

Answer 4

split up 75 into its factors, can you ?

Answer 5

\(\sqrt {75}= \sqrt {...\times ...\times ...}\)

Answer 6

5 and 15?

Answer 7

yeah, but 15 is again split able.

Answer 8

5 * 5 * 3?

Answer 9

and then 5 is a pair so 5√3 right?

Answer 10

yes, now since its a "square" root, you group two numbers and can bring it out of sqrt sign,
\(\sqrt {75}= \sqrt {5\times 5\times 3}=5\sqrt3\)
yes! you got it even before i started explaning :D

Answer 11

so, 15√3 / 5√3 =... ?
we will deal with 'x' separately

Answer 12

3√3
im not sure if it simplifys to 3?

Answer 13

yes, its 3
√3 gets cancelled from numerator and denominator , and 15/5 is just 3

Answer 14

if it is just a plain 3, how do we factor in the x?

Answer 15

we will go for 'x' now.
numerator =x
denominator = \(\sqrt{x^2}\)
can you simplify the denominator ?

Answer 16

i know you can, you have done a similar thing just a few seconds ago...

Answer 17

i think you would either simplify to x or maybe just leave it at √x^2?

Answer 18

one thing to note \(\sqrt{75x^2}=\sqrt {75}\sqrt{x^2}\)
be sure! would it simplify to x ?

Answer 19

oh, so it would just stay the same right? because it cant be factored?

Answer 20

Medal for "split-able" @hartnn :)
@haileemackk some people might be nitpicky... but for instance, what is
\[\huge \sqrt{(-5)^2}\] ?

Answer 21

lol, terenz...
yeah, if you are in doubt, consider 'x' as any number and see what it simplifies to...

Answer 22

Oh, so √75x^2 would be like saying:
√75 * x * x
x√75
?

Answer 23

yes!
which is 5x√3
as already discussed.
so, anything gets cancelled from numerator and denominator ?

Answer 24

My turn to be nitpicky... but isn't
\[\huge \sqrt{x^2}=|x|\]?

Answer 25

yes, but i don't think it should be taken into consideration here, lets keep it simple :)

Answer 26

Agreed. :)

Answer 27

so,\(\sqrt{x^2}=x\)

Answer 28

i dont understand what you mean about anything being cancelled. wouldn't there have to be two of the same thing to cancel each other out?

Answer 29

ok, let me write steps for you.

Answer 30

\(\large \dfrac{15x \sqrt 3}{\sqrt {75x^2}}=\dfrac{15x \sqrt 3}{5x \sqrt3}\)
clear ?

Answer 31

would you cancel 15x√3 out?

Answer 32

First, cancel out what can clearly be cancelled out... things that are exactly the same in the numerator and denominator.

Answer 33

\(\dfrac{15x \sqrt 3}{\sqrt {75x^2}}=\dfrac{3 \times \cancel{5} \cancel{x} \cancel{\sqrt 3}}{\cancel{5}\cancel{x} \cancel{\sqrt3}}\)

Answer 34

Ohhh! okay, so now all we have left is the 3?

Answer 35

thats it!
everything breaks down to just 3 !

Answer 36

Awesome :)

Answer 37

okay, thank you guys so much for all of your help!

Answer 38

you are most welcome ^_^

Answer 39

No problem... though I didn't do much except for minor commentary :)