It looks like you've uploaded a file. Let me extract and analyze the mathematical content in it. I'll process it and provide a detailed response. PIL import Image

Load the image to inspect the contents

img_path = '/mnt/data/1733521725853l1pp57oi.jpg' image = Image.open(img_path)

Display the image to analyze the contents

image.show()I have displayed the image for analysis. To proceed, I will extract the mathematical content from it. Let me process this for you. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(image)

Display the extracted text

extracted_textIt seems like the image contains a question about rationalizing the denominator of a mathematical expression. The text extracted mentions the need to multiply by $\sqrt{5}$, possibly in relation to simplifying an expression that has a square root in the denominator.

To provide a precise answer, could you clarify the exact expression in question? For example, if the denominator involves a square root (like $\frac{1}{\sqrt{7}}$), the goal would be to multiply the numerator and denominator by the conjugate of the denominator (in this case, $\sqrt{7}$) to rationalize it.

Would you like more details or a step-by-step explanation of rationalizing denominators?

Here are some related questions that might help deepen the understanding:

1. What is the general method to rationalize the denominator of a fraction with a square root?
2. How do you simplify expressions involving square roots in the numerator and denominator?
3. What are conjugates, and why are they useful in rationalizing expressions?
4. Can rationalizing the denominator affect the value of an expression?
5. How do you handle cube roots or higher roots when rationalizing denominators?

Tip: When rationalizing, always multiply both the numerator and the denominator by the same expression to maintain the equality of the fraction.