Question

mr. munoz gave his students the following expression to simplify as their exit ticket for class one day.$sqrt{24} + 3.85$julian used a calculator to simplify the expression and determined that the expression simplifies to be a rational number. below is the work he showed on his exit ticket.$sqrt{24} + 3.85 = 4.89898 + 3.85 = 8.74898$determine if julian is correct and provide justification for that conclusion.a. julian is incorrect because $sqrt{24}$ results in a non-repeating, non-terminating decimal. this means it is an irrational number, and the sum will also result in an irrational number.b. julian is incorrect because the result is a repeating decimal. this means that the sum is an irrational number.c. julian is correct because $sqrt{24}$ results in a terminating decimal. this means it is a rational number, and the sum will also result in a rational number.d. julian is correct because the result is a terminating decimal. this means that the sum is a rational number.

Explanation:

Step1: Classify $\sqrt{24}$

$\sqrt{24} = 2\sqrt{6}$, and $\sqrt{6}$ is irrational (non-repeating, non-terminating decimal). Thus $\sqrt{24}$ is irrational.

Step2: Analyze sum of irrational + rational

3.85 is a rational number (terminating decimal). The sum of an irrational number and a rational number is always irrational.

Step3: Evaluate Julian's conclusion

Julian claims the sum is rational, which is incorrect. Match to the correct justification.

Answer:

A. Julian is incorrect because $\sqrt{24}$ results in a non-repeating, non-terminating decimal. This means it is an irrational number, and the sum will also result in an irrational number.