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].

Question

Mathematics

Maximillian Steele

10 April, 06:09

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].

+4

Answers (2)

Know the Answer?

Chester · Answer 1

1. rational

2. irrational

3. irrational

Jaden Roman · Answer 2

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.