How do you simplify #sqrt(8x^2)#?

1 Answer
Sep 28, 2015

Answer:

#sqrt(8x^2) = 2sqrt(2)abs(x)#

Explanation:

#sqrt(8x^2)#
#color(white)("XXX")=sqrt(2^2*2*x^2)#
#color(white)("XXX")=sqrt(2^2)*sqrt(2)*sqrt(x^2)#
#color(white)("XXX")=2sqrt(2)abs(x)#

Note, by convention, #sqrt(q)# for #q in RR^(0+)# is the primary (non-negative) square root and therefore it is necessary to take the absolute value of #x# when evaluating #sqrt(x^2)#