To simplify the expression (√75 + √243 – √48) : √3, we can first simplify each square root individually.

√75 can be simplified as √(25 * 3), which is equal to √25 * √3. The square root of 25 is 5, so √75 simplifies to 5√3.

√243 can be simplified as √(81 * 3), which is equal to √81 * √3. The square root of 81 is 9, so √243 simplifies to 9√3.

√48 can be simplified as √(16 * 3), which is equal to √16 * √3. The square root of 16 is 4, so √48 simplifies to 4√3.

Now, we can substitute these simplified values back into the original expression:

(5√3 + 9√3 - 4√3) : √3

Combining like terms, we have:

(5√3 + 9√3 - 4√3) : √3 = (10√3) : √3

Since the square root of 3 divided by the square root of 3 is equal to 1, we can simplify further:

(10√3) : √3 = 10

Therefore, (√75 + √243 – √48) : √3 simplifies to 10.