Question

If q is rational and s is irrational then q+s, q-s, qs, q/s are irrational

Answer 1

Answer:

Answer is irrational

Hope it will help you

Answer 2

Answer:

Given q is rational and s is irrational

1) The sum of any rational number and any irrational number will always be an irrational number.

1/2 + √3 Is a irrational

So q + s is irrational

2) The difference of a rational and irrational number is always irrational

1/2 - √3 Is a irrational

So q - s is irrational

3) The product of any rational number and any irrational number will always be an irrational number.

For example: 2/3 x √2 = 2√2/3

is an irrational

So qs is irrational

4) the quotient of a nonzero rational number and an irrational number is irrational

So if q is not zero then q/s is irrational

From defintion a=m/n such that m,n∈Z,n≠0.

Take the contrapositive: suppose m/nb∈Q prove m/n∉Q.

Immediate contradiction from defining m,n∈Z,n≠0. Thus m/nb is irrational.