Select from the drop-down menus to correctly complete the proof. to prove that 3√5 is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0. isolating the radical gives √5= a/3b (all one fraction). the right side of the equation is [rational or irational]. because the left side of the equation is [rational or irational], this is a contradiction. therefore, the assumption is wrong, and the number is [rational or irational].

1. rational

2. irrational

3. irrational

Rational; irrational; irrational.

Step-by-step explanation:

a/3b is a rational number, as it is represented by a fraction and b ≠ 0.  This means the first blank is "rational."

√5 is an irrational number.  This means the second blank is "irrational."

Since we have an irrational number set equal to a rational number, this is a contradiction.  This means our original assumption is wrong, and the number is irrational.  This is the third blank.