SOLUTION: What is the square root of 180 written in simplest radical form?
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Question 247361: What is the square root of 180 written in simplest radical form?
Found 3 solutions by College Student, checkley77, solver91311:
Answer by College Student(505) (Show Source): You can put this solution on YOUR website!
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
SQRT180=SQRT(36*5)=6SQRT5 ANS.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You need the prime factorization of 180 to start.
180 is divisible by 2, 180/2 = 90; one factor of 2
90 is divisible by 2, 90/2 = 45; two factors of 2
45 is not divisible by 2, but 4 + 5 = 9 is divisible by 3, so 45 is divisible by 3, 45/3 = 15, one factor of 3
15 is divisible by 3, 15/3 = 5, two factors of 3
5 is prime.
So the prime factorization of 180 is 
Now you can write:
But that can be written:
\left(\sqrt{3\,\times\,3}\right)\left(\sqrt{5}\right)\ =\ 2\,\cdot\,3\,\cdot\sqrt{5}\ =\ 6\sqrt{5})
John
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