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Here each square root radical should be simplified further.

√12 = √(2 * 2 * 3). Now pull out the number which is repeating twice inside the radical.

This gives:

So, √12 + √243 = 2√3 + 9√3 = (2 + 9) √3 = 11√3.

(Since they have the same radical √3, hence they are like terms and can be added).

Hence the value of the expression, √12+ √243 is = 11√3.

Here each square root radical should be simplified further.

√48 = √(2 * 2 * 2 * 2 * 3). Now pull out the number which is repeating twice inside the radical.

This gives:

So, √243 - √48 = 9√3 -4√3 = (9 - 4) √3 = 5√3.

(Since they have the same radical √3, hence they are like terms and can be subtracted).

Hence the value of the expression, √243- √48 is = 5√3.