Yes.
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Such a sum is always rational.
The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero.
Yes, for example, square root of 2 x square root of 2 = 2.* * * * *No, the product of two rational numbers must always be rational.No.Proof :If you take rational number a/b and multiply by rational c/d you get ac/bd.Since ac and bd are each integral, the product is rational.
The product of 2 rationals must be rational. The product of a rational and an irrational is irrational (unless the rational is 0) The product of two irrationals can be either rational or irrational.
You get a product which can be rational or irrational.