Answer:1. 0
2. see below
Step-by-step explanation:
3 sqrt(128) - 2 sqrt(6) * 4 sqrt(3)
3 sqrt(128) - 8 sqrt(6*3)
3sqrt(128) - 8 sqrt(18)
3 sqrt(64*2) - 8 sqrt(9*2)
3 sqrt(64)sqrt(2) - 8 sqrt(9) sqrt(2)
3 * 8 * sqrt(2) - 8 * 3 * sqrt(2)
24 sqrt(2) - 24 sqrt(2)
0
2. 5 is rational
-3sqrt(8) = -3 sqrt(4) sqrt(2) = -3 * 2 sqrt(2) = -6 sqrt(2) is irrational
addition: when you add a rational plus an irrational, you get an irrational
5 + -6 sqrt(2) = irrational
subtraction : when you subtract a ration and an irrational, you get an irrational
5 - -6 sqrt (2) = 5 + 6 sqrt(2) = irrational
multiplication: when you multiply a rational and an irrational, you get an irrational
5 * -6sqrt(2) = -30 sqrt(2) = irrational
division: when you divide a rational by an irrational, you will get an irrational
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