Simplify 5 square root of 7 end root plus 12 square root of 6 end root minus 10 square root of 7 end root minus 5 square root of 6. 5 square root of 14 end root minus 7 square root of 12 5 square root of 7 end root minus 7 square root of 6 7 square root of 12 end root minus 5 square root of 14 7 square root of 6 end root minus 5 square root of 7

[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]