Question

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.

Answer 1

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