is the mam al sqrt (2)+sqrt (4) work to support then claim is shown below an indicate whether the mident has provided correct rountaining ha support his Inday classes that the somal sqrt (2)+sqrt (4) because sqrt (4)=2 and sqrt (2)+2=sqrt (2+2)=sqrt (4)=2 tharelora sqrt (2)+sqrt (4)=2 is an intrger which Their chairs that the sum rid sqrt (2)+sqrt (4)=sqrt (2)+2 is an irrational number because ill y=(sqrt (2)+2) and y is a rational number then 1.2 number, but sinca p-2-(sqrt (2)+1)-2=sqrt (2) and sqrt (2) is an inational number,number. ol sqrt (2)+sqrt (4) an inakonal number becabue sqrt (2)+sqrt (4)=sqrt (2)+2=2sqrt (2) and although? is a rational number. sqrt (2) is ani erational number and therefore 2sqrt (2) 2times sqrt (2) is an imalional number.

The student has not provided sufficient support for their claim that $\sqrt{2} + \sqrt{4}$ is an integer. Let's analyze the given information:<br /><br />1. $\sqrt{4} = 2$, which is correct.<br />2. $\sqrt{2} + 2 = \sqrt{2+2} = \sqrt{4} = 2$, which is incorrect. The correct calculation should be $\sqrt{2} + 2 = \sqrt{2} + 2$, which is not equal to $\sqrt{4}$.<br /><br />Therefore, the student's claim that $\sqrt{2} + \sqrt{4} = 2$ is incorrect.<br /><br />To determine whether $\sqrt{2} + \sqrt{4}$ is a rational or irrational number, we need to consider the properties of rational and irrational numbers.<br /><br />A rational number can be expressed as a fraction, where the numerator and denominator are both integers. An irrational number cannot be expressed as a fraction and has a non-repeating, non-terminating decimal expansion.<br /><br />In this case, $\sqrt{2}$ is an irrational number because it cannot be expressed as a fraction and has a non-repeating, non-terminating decimal expansion. $\sqrt{4}$, on the other hand, is a rational number because it can be expressed as the fraction $2/1$.<br /><br />When we add $\sqrt{2}$ and $\sqrt{4}$, we get $\sqrt{2} + 2$. Since $\sqrt{2}$ is irrational and $2$ is rational, their sum is also irrational. Therefore, $\sqrt{2} + \sqrt{4}$ is an irrational number.<br /><br />In conclusion, the student's claim that $\sqrt{2} + \sqrt{4}$ is an integer is incorrect. The correct answer is that $\sqrt{2} + \sqrt{4}$ is an irrational number.