How do you simplify #sqrt(432)#?

2 Answers
Aug 20, 2016

Answer:

#sqrt(432) = 12sqrt(3)#

Explanation:

#432 = 2^4*3^3 = 2*2*3*2*2*3*3 = 12^2*3#

So we find:

#sqrt(432) = sqrt(12^2*3) = sqrt(12^2)*sqrt(3) = 12sqrt(3)#

Aug 20, 2016

Answer:

#12sqrt3#

Explanation:

Let us factorize given the number #432#. For an even number #2# is a factor

#432/2=216#
#216/2=108#
#108/2=54#
#54/2=27#
we observe that #3# is a factor
#27/3=9#
#9/3=3#
#:.432=2xx2xx2xx2xx3xx3xx3#
#=>sqrt432=sqrt(2xx2xx2xx2xx3xx3xx3)#
paring and taking one digit for each pair out of the square root sign we get
#sqrt432=sqrt(bar(2xx2)xxbar(2xx2)xxbar(3xx3)xx3)#
#=>sqrt432=2xx2xx3sqrt3#
#=>sqrt432=12sqrt3#