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How do you rationalize #(2sqrt(180y))/540#?

Answer 1

Avery Alexander

Let's start by factorizing:

#180=(2xx2)xx(3xx3)xx5# #540=2xx2xx3xx3xx3xx5#

Now that we have removed all of the "doubles" from the root:

#=(cancel2xxcancel3sqrt(5y))/(cancel2xx2xxcancel3xx3xx3xx5)=sqrt(5y)/90#

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Answer 2

Savannah Anderson

To rationalize the expression (2√(180y))/540, we can simplify it by first simplifying the square root of 180y. The square root of 180 can be simplified as 6√5, so the expression becomes (2 * 6√5√y)/540. Simplifying further, we get (12√(5y))/540. Finally, we can simplify this expression by dividing both the numerator and denominator by their greatest common factor, which is 12. This gives us √(5y)/45 as the rationalized form of the expression.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.