78.9k views
0 votes
Select from the drop-down menus to correctly complete the proof.

To prove that 2√⋅7 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 2√= a/7b. The right side of the equation is(irrational, rational). Because the left side of the equation is(irrational, rational), this is a contradiction. Therefore, the assumption is wrong, and the product is(rational, irrational).

User Ljuk
by
8.3k points

1 Answer

0 votes

We need to prove 2*√7 is an irrational number.

Steps:

1) To prove that 2√7 is an irrational, assume the product is rational and set it equal to a/b , where b is not equal to 0.

2) Isolating the radical gives 2= a/√7b.

3) The right side of the equation is irrational.

4) Because the left side of the equation is rational, this is a contradiction.

5) Therefore, the assumption is wrong, and the product is irrational.

User Salvi Shahzad
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories