How do you simplify #8 sqrt (19s) - 8 sqrt(10d) - 4 sqrt( 19s) - 8 sqrt (10d)#?

1 Answer

Answer:

#4sqrt(19s)-16sqrt(10d)#

Explanation:

Let's first look at the terms within the square roots themselves:

#19s# and #10d#

There is nothing within the roots that can be simplified - no squares under the root that can be extracted (unlike, for example, #sqrt4# which equals 2).

So what we're really talking about here is two complicated looking terms: #sqrt(19s)# and #sqrt(10d)# and different coefficients of them. So how about if we change the complicated looking terms and substitute in something easier to work with:

#A=sqrt(19s)#
#B=sqrt(10d)#

which gets us:

#8A-8B-4A-8B#

which gives us:

#4B-16B#

and now we can put in the original terms:

#4sqrt(19s)-16sqrt(10d)#