No
![6\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/3ousu1ssk7ul0x4rs10ccxctvi2l6rqb9u.png)
Step-by-step explanation
Step 1
let the given expression
![\sqrt[]{72}](https://img.qammunity.org/2023/formulas/mathematics/college/r2wj1sbwqopwscov9i47onppx2c9nreutk.png)
the firs thing to do is to get the prime factors of 72, so
a) prime factors

Step 2
now we know that:
![\begin{gathered} \sqrt[n]{a^n}\text{ =a} \\ \text{and} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/t68h50716qmgjoqwzz7igjvo30eocokaaj.png)
so
![\begin{gathered} \sqrt[]{72}=\sqrt[]{2\cdot2^2\cdot3^2} \\ \sqrt[]{72}=\sqrt[]{2}\sqrt[]{2^2}\sqrt[]{3^2} \\ \sqrt[]{72}=2\cdot3\sqrt[]{2} \\ \sqrt[]{72}=6\sqrt[]{2} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/pf0rzj8mcl5rws11f0zlpkx9tlpldanqj1.png)
therefotre:
Darrin was wrong because his expression was not totally simplified, the full simplification is
![6\sqrt[]{2}](https://img.qammunity.org/2023/formulas/mathematics/college/3ousu1ssk7ul0x4rs10ccxctvi2l6rqb9u.png)
I hope this helps you