How do you simplify #4+sqrt200 + 8sqrt49 - 2sqrt2#?
1 Answer
Oct 9, 2015
Explanation:
Your starting expression looks like this
#4 + sqrt(200) + 8sqrt(49) - 2sqrt(2)#
The first thing to notice here is that
#49 = 7 * 7 = 7^2#
This means that the expression can be first simplified to
#4 + sqrt(200) + 8 * sqrt(7^2) - 2sqrt(2)#
#4 + sqrt(200) + 8 * 7 - 2sqrt(2)#
#4 + sqrt(200) + 56 - 2sqrt(2)#
#60 + sqrt(200) - 2sqrt(2)#
Now take a look at
#200 = 100 * 2 = 10^2 * 2#
This means that you have
#60 + sqrt(10^2 * 2) - 2sqrt(2)#
#60 + 10sqrt(2) - 2sqrt(2)#
#60 + 8sqrt(2)#
Finally, use
#60 + 8sqrt(2) = color(green)(4 * (15 + 2sqrt(2)))#