[tex]5 \sqrt{7} + 12 \sqrt{6} -10 \sqrt{7} - 5 \sqrt{6} [/tex]
Think of square roots of the same numbers as being like terms.
Think of
5x + 12y - 10x - 5y =
= 5x - 10x + 12y - 5y
= -5x + 7y
Think of sqrt(7) as x, and sqrt(6) as y.
[tex]5 \sqrt{7} + 12 \sqrt{6} -10 \sqrt{7} - 5 \sqrt{6} =[/tex]
[tex]=5 \sqrt{7} -10 \sqrt{7} + 12 \sqrt{6} - 5 \sqrt{6} [/tex]
[tex]=-5 \sqrt{7} + 7 \sqrt{6} [/tex]
[tex]= 7 \sqrt{6} - 5 \sqrt{7} [/tex]
