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Based on the what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of numbers y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number

Based on the what we established about the classification of y and using the closure of integers what does the equation tell you about the type of numbers y mus class=

Respuesta :

varshamittal029

The statements are:

x . y = m/n

substituting the values.

a/b . y = m/n

multiplication property of equality.

b/a . a.b . y  = m/n . b/a

simplify.

y = mb/na

The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.

Hence we made the required conclusion.

Learn more about rational numbers here:

brainly.com/question/1535013

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