How do you find the square root of 405?

1 Answer
Alan P.
Sep 16, 2015

#sqrt(405) = 9sqrt(5)#

Explanation:

Taking the prime factors of #405#:

#=3xx135#
#=color(red)(3xx3)xx45#
#=color(red)(3xx3)xx3xx15#
#=color(red)(3xx3)xxcolor(blue)(3xx3)xx5#
#=color(red)(3^2)xxcolor(blue)(3^2)xxcolor(green)(5)#

#sqrt(405)#

#=sqrt(color(red)(3^2)*color(blue)(3^2)*color(green)(5)#
#=sqrt(color(red)(3^2))*sqrt(color(blue)(3^2))*sqrt(color(green)(5))#
#=color(red)(3)*color(blue)(3)*sqrt(color(green)(5))#
#=9sqrt(5)#

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