How do you simplify # sqrt12*sqrt10#?

2 Answers
Apr 22, 2016

#=sqrt(2^2*3)sqrt10=2sqrt3*sqrt10=2sqrt30#

Apr 22, 2016

Answer:

Very slightly different presentation
#2sqrt(30)#

Explanation:

Look for common values that are in both roots. If we can find values that end being squared we can 'take them outside' the square roots.

Given:#" "sqrt(12)sqrt(10)#

Whole number factors of 12 are:
{1,12}, {2,6}, {3,4}#" "# Note that {3,4}#->{3, 2^2}#

Whole number factors of 10 are:
{1, 10}, {2,5}
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I can not spot any other possible useful combination than the following.

Write as:#" "sqrt(3xx2^2)xxsqrt(10)#

#2sqrt(3)xxsqrt(10)#

#2sqrt(3xx10)#

#color(blue)(=2sqrt(30))#