What do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.

the product of a nonzero rational and an irrational is irrational.

let a/b be the rational number and x the irrational.

let us assume that a rational times an irrational number gives a rational number.

so we assume multiplying   a/b * x = m/n where m and n are integers.

making x the subject my multiplying both sides by b/a we get:

x = mb/an   which is   rational. because m, b , a and n are integers

but we assumed x   is irrational but we have proved it rational. so that is our contradiction.

so our assumption was wrong and rational * irrational must be irrational.

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)

answer:   b

step-by-step explanation:

x2 = 16

x can not be a negative number because 16 is positive

the only answer would be positive 8