How do you simplify 5 square root of 243?

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Answer 1 · 2018-03-20T02:11:48

The simplified radical is #45sqrt(3)#.

First, we need to write the English statement in "math form":

#overbrace"5"^(5xx) overbrace"square root of"^(sqrtcolor(white)x) overbrace"243"^(quad243quad)#

To simplify this, factor #243# into some square numbers that we know:

#color(white)=5xxsqrt243#

#=5xxsqrt(color(red)81*3)#

#=5xxsqrt(color(red)(9^2)*3)#

#=5xxcolor(red)9xxsqrt(3)#

#=45xxsqrt(3)#

#=45sqrt(3)#

This is the simplified radical. Hope this helped!