Question

question 10 (1 point) (03.01 mc) solve 4√6 + 8√4 and explain whether the answer is rational or irrational. a the answer 12√10 is rational because the sum of a rational number and irrational number is a rational number. b the answer 4√6 + 16 is irrational because the sum of a rational number and irrational number is an irrational number. c the answer 12√10 is irrational because the sum of a rational number and irrational number is an irrational number. d the answer 4√6 + 16 is rational because the sum of a rational number and irrational number is a rational number.

Explanation:

Step1: Recall the property of rational and irrational numbers

The sum of a non - zero rational number and an irrational number is an irrational number. Here, 8 is rational and \(4\sqrt{6}\) is irrational. Also, 4 is rational and \(4\sqrt{6}\) is irrational.

Step2: Analyze the sum \(4\sqrt{6}+8\sqrt{4}\)

First, simplify \(8\sqrt{4}=8\times2 = 16\). The expression becomes \(4\sqrt{6}+16\). Since \(\sqrt{6}\) is irrational and 16 is rational, the sum \(4\sqrt{6}+16\) is irrational.

Answer:

b. The answer \(4\sqrt{6}+16\) is irrational because the sum of a rational number and irrational number is an irrational number.