Question

Rationalize the denominator
square root of 20/x

Answer 1

are you asking \(\large\sqrt{\frac{20}{x}}\)

Answer 2

yes

Answer 3

i have the answer, i just don't know how to get it

Answer 4

Well, I was going to say I dont know what exactly they're wanting, because it doesnt really make sense...

Answer 5

\[2\sqrt{5}\sqrt{x^{-1}}\] is how I would answer, but its not "Rationalizing the denominator"

Answer 6

\[\frac{ 2\sqrt{5x} }{ x }\] is the answer

Answer 7

i just don't get why x is in the numerator

Answer 8

I got there like this:
\[\sqrt{\frac{20}{x}} = \sqrt{20}\sqrt{-1} = 2\sqrt{5} \sqrt{x^{-1}}\]

Answer 9

Well, I suppose it's true if x is always positive... but it's technically wrong.

Answer 10

thank you for your help!

Answer 11

\[\sqrt{\frac{20}{x}}=\frac{\sqrt{20}}{\sqrt{x}} = \frac{2\sqrt{5}}{\sqrt{x}}\]

Answer 12

YESSS that has to be right.

Answer 13

that x with the 5 is to keep it from being 0/0

Answer 14

but technically, they arent the same.

Answer 15

so does the x have to be written?

Answer 16

I mean, if you're instructor requires it... lol

Answer 17

If x is not a perfect square the denominator will be irrational, so multiplying and dividing by a factor of square root of x will rationalize the denominator

Answer 18

Feels rather unnecessary though