What is the exact value of the expression the square root of 486. - the square root of 24. + the square root of 6.? Simplify if possible.

Sqrt (486) - sqrt (24) + sqrt (6)

find the factors of 486 that we can remove from under the square root sign

2 * 243

2 * 3 * 81

2 * 3 * 9 * 9 (we have 2 nines, we can move a 9 outside the sqrt sign)

sqrt (486) = 9 sqrt (6)

Repeating for sqrt (24)

2 * 12

2 * 2 * 6

2 * 2 * 2 * 3 (we can move a 2 outside the sqrt

sqrt (24) = 2 sqrt (6)

Finally, add all 3 terms together

9 sqrt (6) - 2 sqrt (6) + sqrt (6)

8 sqrt (6)

8 times square root of 6 is the final answer