How do you simplify #sqrt192#?

1 Answer
Mar 7, 2018

Answer:

#sqrt(192)=8sqrt(3)#

Explanation:

By observation,
or proceeding slowing by extracting smallest factors:
#192#
#color(white)("XXX")=2 * 96#
#color(white)("XXX")=2^2 * 48#
#color(white)("XXX")=2^2 * 2 * 24#
#color(white)("XXX")=2^2 * 2^2 * 12#
#color(white)("XXX")=2^2 * 2^2 * 2 * 6#
#color(white)("XXX")=2^2 * 2^2 * 2^2 * 3#
#color(white)("XXX")=(2^3)^2 * 3#
#color(white)("XXX")=8^2 * 3#

Therefore
#sqrt(192)=sqrt(8^2 * 3) = 8sqrt(3)#