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# Let a be a rational number and b be an irrational number. Which of the following are true statements?(there is more than 1 answer) A.) the sum of a and b is never rational B.) The product of a and b is rational C.) b^2 is sometimes rational D.) a^2 is always rational E.) square root of a is never rational F.) square root of b is never rational

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A.) the sum of a and b is never rational.This is a true statement. From an irrational umber has a decimal part is infinite and non-periodic, when you add a rational number to an irrational number, the result will have the same infinite non-recurring decimal part, so that the new number will be irrational.B.) The product of a and b is rationalThis is false. The zero is a rational number, and when you multiply an irrational number by zero, the result is always zero.C.) b^2 is sometimes rationalThis is true. When you square an irrational number that comes from a square root like , you will end up with a rational number , but, if the square rational of different roots of the square root as , you will end up with an irrational number: . D.)^2 is always rationalThis is false. If you square a rational number, always end up with another rational number.E.) square root of a is never rationalThis is false. The square root of perfect squares are always rational numbers: , ,...F.) square root of b is never rationalThis is true. Since the square root of any non-perfect square number is irrational, and all the irrational numbers are not perfect squares, the square root of an irrational number is always irrational.We can conclude that since a is a rational number and b an irrational number, a, C, D, and F is the pure truth.