How do you find 2 sqrt 325?

1 Answer
Alan P.
Sep 9, 2015

Assuming we are dealing with only the principal square root:
#color(white)("XXX")2sqrt(325)=10sqrt(13)#
Using a calculator we could further evaluate this as #36.05551#

Explanation:

#325 = 5xx5xx13#

So
#color(white)("XXX")sqrt(325) = sqrt(5^2xx13) = sqrt(5^2)*sqrt(13) = 5sqrt(13)#
and
#color(white)("XXX")2sqrt(325) =2xx5sqrt(13)=10sqrt(13)#

The simplest way to find an approximation for the irrational value #sqrt(13)# is to use a calculator.

If we are not restricted to the principal square root then #-10sqrt(13)# is another solution.

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