## Intermediate Algebra: Connecting Concepts through Application

It can be seen that Mark incorrectly simplified the square root of 10 to 5. The correct answer is $xy^{4}\sqrt {10}$.
Step 1: We will solve the expression to find the correct answer and to determine Mark's mistake. Step 2: $\sqrt {10x^{2}y^{8}}$ Step 3: $\sqrt {10}\times\sqrt {x^{2}}\times\sqrt {y^{8}}$ Step 4: $\sqrt {10}\times(x)^{2\times\frac{1}{2}}\times (y)^{8\times\frac{1}{2}}$ Step 5: $\sqrt {10}\times(x)\times (y)^{4}$ Step 6: Therefore, the correct answer is $xy^{4}\sqrt {10}$. Step 7: It can be seen that Mark incorrectly simplified the square root of 10 to 5.