Discuss: Sums and Products of Rational and Irrational Numbers Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?

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Jyotsana PrakashLv10

20 Mar 2021

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The closure properties for a set of numbers assure that the sumand product of two numbers in a given set of numbers are also inthe set of numbers. Determine whether each set ofnumbers is closed for addition, for multiplicaiton, or forboth. If not, give a counterexample.

a) rational numbers

b) negative numbers

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Solve Diophantusâs Problem Bâ8: To find two numbers
such that their difference and the difference of their cubes
are equal to two given numbers. (Write the equations as
x â y = a, x3 â y3 = b. Diophantus takes a = 10, b =
2120.) Derive necessary conditions on a and b that ensure
a rational solution.

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