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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