How do you simplify #(3+sqrt32)-(4+2sqrt98)#?

1 Answer
May 10, 2018

Answer:

#-1-10sqrt2#

Explanation:

Original Question: #(3+sqrt(32))-(4+2sqrt98)#

Distribute the negative so you have:
#3+sqrt(32)-4-2sqrt98 = -1 + sqrt(32)-2sqrt(98)#

Simplify the radicals
#-1+sqrt(16xx2)-2sqrt(49xx2)#
#= -1 + sqrt(4^2xx2)-2sqrt(7^2xx2)#
#= -1 + sqrt(4^2)*sqrt2-2sqrt(7^2)*sqrt2#
#= -1+4sqrt2-2*7sqrt2#
#= -1 + 4sqrt2-14sqrt2#

Since #4sqrt2# and #-14sqrt2#, we can subtract the two terms.
#=-1-10sqrt2#