Question

PLZ HELP WITH THIS ALGEBRA IVE BEEN WAITING FOREVER FOR SOMEONE TO HELP ME! equation is below

Answer 1

\[\frac{ 4\sqrt{150} }{ \sqrt{189x} }\]

Answer 2

i can give the answer choices if needed

Answer 3

multiply each side by \[\frac{ \sqrt{189x} }{ \sqrt{189x} }\]

Answer 4

multiply the numerator of the origanal fraction by that?

Answer 5

please help

Answer 6

What are your answer choices? I can't decide what our end-goal is supposed to be.

Answer 7

here they are:
a 20 sqrt(14x)/21x
b 4/sqrt(39x)
c 4 sqrt(39x)/189x
d 16/189x

Answer 8

are you typing?

Answer 9

ou can simplify sqrt(150) and sqrt(189) by breaking it into its prime factorization.
For example, 150 = 25 * 6 = 5^2 * 3 * 2
And 189 = 9 * 21 (add the digits to see it is divisible by 9), = 3^2 * 3 * 7

Perfect squares fall out of the radicals. \(\sqrt{a^2} = a \) and we can break up factors under a radical using this property:
\( \sqrt{ab} = \sqrt{a} \sqrt{b} \)

\( \dfrac{4 \sqrt{150}}{\sqrt{189 x}} = \dfrac{4 \sqrt{5^2} \sqrt{3} \sqrt{2}}{\sqrt{3^2} \sqrt{3} \sqrt{7} \sqrt{x}} \)

Answer 10

so what happens after you break it up?

Answer 11

The sqrt(3) in the numerator and denominator cancel; sqrt(5^2) = 5, sqrt(3^2) = 3, and that leaves:
\( \dfrac{ 4 \sqrt{150}}{\sqrt{189x}} = \dfrac{ 4*5 * \sqrt{2}}{3* \sqrt{7x}} \)
Now you can multiply numerator and denominator by the sqrt(7x) to get rid of the radical in the denominator. Sorry this is a lot that I am loading onto each post at once. I can go back and explain anything needed.

Answer 12

so i just simlify 4*5* sqrt of 2

Answer 13

When you multiply both numerator and denominator by sqrt(7x), your denominator does not vanish; it just loses the radical sign. The leftover in the denominator is 3 * 7x = 21x.

Answer 14

And the numerator is 4 * 5 * sqrt(2) * sqrt(7x)

Answer 15

the only answer that has denominator 21 x is answer a?

Answer 16

Answer A looks correct.
But yes, you should always break numbers into their prime factorizations, and then multiply both numerator and denominator by the remaining radical on the denominator. That should make the arithmetic simpler in the end.

Answer 17

Ok thank you so much could you help me with one more?

Answer 18

Sure, you can post it here or in a new question. :)

Answer 19

simplify \[\frac{ 4 \sqrt{6} }{ \sqrt{30} }\] by rationalizing the denominator. Show the work

Answer 20

If you can tell im not good with the rational expression stuff :/

Answer 21

@Darealest123 : You've posted multiple threads for this same question (which was addressed by AccessDenied in this thread) - it'd be better if there was only 1 thread, else others may post responses in other threads, awaiting your feedback.

Answer 22

i closed the others and posted it again because i already bumped the original multiple times

Answer 23

Well, I posted a response in a separate thread which you opened and was awaiting your feedback when I noticed that you had now opened this thread.

Answer 24

oh i closed all the previous ones so i dont know how that happened

Answer 25

Never mind. Anyway, an important point to note about rationalizing fractions is to remove all radicals in the denominator. We often do this by multiplying by the radical in the denominator. Why don't you try this approach with the question you have just posed in this thread?