Help please Im trying to learn

Question

help please Im trying to understand it but can’t seem to get it.

Given two real numbers a and b, determine the type of solution (s) for each given situation.

situation 1: if a=6 and b=1/(√3) find the product and express your solution in simplest form.

Situation 2: if a and b are rational numbers, will their product be rational or irrational? Explain

Situation 3: if a and b are rational numbers, will their sum be rational or irrational? Explain

Answer 1

(1)

Rationalize the expression.

ab = 6(1/√3) = 6(1/√3) (√3 / √3) = 6 √3 / 3 = 2√3

(2)

a = m/n, both m and n integers

b = p/q, both p and q integers

ab = mp / nq

Both mp and nq are integers, so a/b is rational.

(3)

a + b = m/n + p/q = (mq + np) / (nq)

Both (mq + np) and nq are integers, so (a + b) is rational.