SOLUTION: Here is my problem: My problem is asking me to rationalize the denominator and simplify the sqrt(45/x). I have tried to multiply the 45 with a 5 to simplify it, but that didn't wor

Question 613663: Here is my problem: My problem is asking me to rationalize the denominator and simplify the sqrt(45/x). I have tried to multiply the 45 with a 5 to simplify it, but that didn't work. Tried to figure out a way to get the x from the denominator, nothing worked. I remember learning about these kinds of problems in my old Algebra class but I completely forgot how to do them. Can you help me with this?
Found 2 solutions by solver91311, Theo:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First thing is that 45 is equal to 5 times 9, so

To rationalize a single term denominator, multiply your fraction by 1 in the form of the denominator divided by itself.

See my lesson on rationalizing denominators

John

My calculator said it, I believe it, that settles it

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
expression is:
sqrt(45/x)
this is equivalent to sqrt(45) / sqrt(x)
multiply both denominator and numerator by sqrt(x) and you'll get:
(sqrt(45) * sqrt(x) / (sqrt(x))^2
since (sqrt(x))^2 is equal to x, then the expression becomes:
(sqrt(45) * sqrt(x) / x
sqrt(45) is the same as sqrt(5*9) which is the same as 3*sqrt(5).
your expression becomes:
(3*sqrt(5)*sqrt(x))/x
this can be simplified further to:
(3*sqrt(5x))/x
i don't think it can be simplified further.
test your solution by randomly picking a value for x and see if the original expression yields the same answer as the final expression.
example:
x = 3
original expression of sqrt(45/x) becomes sqrt(45/3) becomes 3.87298....
final expression of (3*sqrt(5x))/x becomes (3*sqrt(15)/3) becomes 3.87298...
the answer is the same so the expressions can be reasonably assumed to be equivalent.

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