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Before we begin, we want to work with sqrt(48) alone for a moment:

sqrt(48) = sqrt(4 x 12) = sqrt(4 x 4 x 3) = 4 sqrt(3) .

Now, with sqrt(12) alone:

sqrt(12) = sqrt(4 x 3) = 2 sqrt(3).

Now we can plug both of those into the big expression given in the question:

9 sqrt(48) + 3 sqrt(12) = 9 [ 4 sqrt(3) ] + 3 [ 2 sqrt(3) ] =

[ (9 x 4) + (3 x 2) ] sqrt(3) = [ 36 + 6 ] sqrt(3) = 42 sqrt(3)

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Q: What is 9 square root of 48 plus 3 square root of 12?
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