Question

Simplify 5 square root of 11 end root minus 12 square root of 11 end root minus 2 square root of 11. negative 33 square root of 9 negative 11 square root of 9 negative 9 square root of 11 negative 9 square root of 33

Answer 1

As long as your indexes are the same (which they are; they are all square roots) and you radicands are the same (which they are; they are all 11), then you can add or subtract.  The rules for adding and subtracting radicals are more picky than multiplying or dividing.  Just like adding fractions or combining like terms.  Since all the square roots are the same we only have to worry about the numbers outside.  In fact, it may help to factor out the sqrt 11: $(5-12-2) \sqrt{11}$.  The numbers subtract to give you -9.  Therefore, the simplification is $-9 \sqrt{11}$