How do you simplify sqrt(2205)?

1 Answer
Zor Shekhtman
Jan 25, 2016

21sqrt(5)

Explanation:

The key to this solution is to represent 2205 as a product of some numbers that are squares of some other numbers and to use a property of square roots that allows to do the following for any two non-negative real numbers X and Y:
sqrt(X*Y) = sqrt(X)*sqrt(Y)

Using this, we can perform the following steps:
sqrt(2205) = sqrt(9*245) =
= sqrt(9)*sqrt(245) =
= sqrt(9)*sqrt(49*5) =
= sqrt(9)*sqrt(49)*sqrt(5) =
= 3*7*sqrt(5) = 21sqrt(5)

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