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Is the sum of two irrational numbers necessarily irrational?
Yes, as long as the two are not mutual resiprocals.
How many 12 W resistors each of the same resistance must be used to produce an equivalent 3.2k ohms 3.0 W resistor if they are connected in parallel?
NOT Possible. In a parallel combination the power tollerence has to increase, thus for every additional resistor in parallel the effective power capacity of the resister would be n(12) Watts where n is the number of resistors connected. ie. if n=3 the power of the combination would rise to 12 x 3 = 36W. Also it is not possible to compute the effective resistance of the combination unless the resitance value of the resitors utilised is known. The question is therefore invalid.
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