Question

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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).

Answer 1

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.