What is 180 as product of prime factors and 180 as a square root?

180 = 2*90
90 = 2*45
45 = 3*15
15 = 3*5
The prime factors are 2, 2, 3, 3, 5

Alternatively, you can draw up a factor tree like what you see in the attached image. The prime numbers are in the red boxes.

Either way, the prime factorization is 
180 = 2*2*3*3*5
which can be written as
180 = 2^2*3^2*5

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As for your second question, are you looking to simplify the square root of 180? If so, then follow these steps

sqrt(180) = sqrt(2*2*3*3*5)
sqrt(180) = sqrt(2^2*3^2*5)
sqrt(180) = sqrt((2*3)^2*5)
sqrt(180) = sqrt((2*3)^2)*sqrt(5)
sqrt(180) = 2*3*sqrt(5)
sqrt(180) = 6*sqrt(5)

sqrt stands for "square root"