How do you rationalize the denominator and simplify #(-24sqrt45)/(72sqrt20)#?

Question

Genesis Allen · Accepted Answer

#-1/2#

First, simplify as much as possible:

#(-24sqrt45)/(72sqrt20#

#24/72=1/3#, so

#(-sqrt45)/(3sqrt20#

Simplify the radicals as much as possible:

#45=3*3*5# #sqrt 45=3sqrt5#

#20=2*2*5# #sqrt20=2sqrt5#

Replace:

#(-3sqrt5)/(3*2sqrt5#

Simplify:

#-(1)/(2#

Savannah Anderson · Answer

undefined To rationalize the denominator and simplify the expression (-24sqrt45)/(72sqrt20), we can start by simplifying the square roots. The square root of 45 can be simplified as the square root of 9 times the square root of 5, which is 3sqrt5. Similarly, the square root of 20 can be simplified as the square root of 4 times the square root of 5, which is 2sqrt5.

Now, the expression becomes (-24 * 3sqrt5) / (72 * 2sqrt5).

Next, we can simplify the expression further by canceling out common factors. The numerator can be simplified as -72sqrt5, and the denominator can be simplified as 144sqrt5.

Finally, we can divide both the numerator and denominator by 72 to simplify the expression even further. This gives us -sqrt5 / 2sqrt5.

Since the square root of 5 divided by the square root of 5 is equal to 1, the expression further simplifies to -1/2.

Therefore, the rationalized and simplified form of (-24sqrt45)/(72sqrt20) is -1/2.