It seems like you've uploaded an image with several math problems. Let me review the content and work through the questions.

I'll start with analyzing the image to provide the necessary solutions. PIL import Image

Load and display the uploaded image to examine the content

img_path = "/mnt/data/1740085881124rk7m9r30.jpg" img = Image.open(img_path) img.show()I’ve reviewed the image you uploaded, which contains several math problems. Here's the breakdown of the problems:

1. Problem 7: Insert the factors under the square root:

   • $(4 - a) \sqrt{a - 5}$
   • $(x + 1) \sqrt{x + 4}$

2. Problem 8: Simplify the expression: $\left( \frac{\sqrt{8/x + 12}}{\sqrt{8/x + 4}} - \frac{\sqrt{8/x - 4}}{\sqrt{8/x - 4}} + \frac{4}{4\sqrt{x - 16}} \right) \div \frac{15}{4\sqrt{x - 16}}$

3. Problem 9: Prove that the value of the expression $3\sqrt{19} + 9\sqrt{6} + 3\sqrt{19} - 9\sqrt{6}$ is an integer.

Would you like me to solve these problems step-by-step? Let me know if you want detailed solutions for any of them!