Show that sum, difference, product and quotient of two rational numbers are still rational, that is, for any x, y ∈ Q, show that x + y, x − y, xy, x y are rational numbers. (2) Show that √ p is irrational for any prime number p. (3) Use (1) and (2) to show that √ 2 + √ 3 is irrational.

Ageologist had two rocks on a scale that weighed 4.6 kilograms together. rock a was 0.5 of the total weight. how much did rock a weigh?

Handsome jack is buying a pony made of diamonds. the price of the pony is p dollars, and jack also has to pay a 25% diamond pony tax. which of the following expressions could represent how much jack pays in total for the pony?

The volume, v, of a rectangular prism is determined using the formula, where / is the length, w is the width, and his theheight of the prism. carltren solves for w and writes the equivalent equation w=using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches?