https://r2.erweima.ai/mathbot/image/17245939571966b13dji7.jpg

# Let's load the image and extract its content using OCR to solve the math problem.
from PIL import Image
import pytesseract

# Load the image
image_path = "/mnt/data/17245939571966b13dji7.jpg"
image = Image.open(image_path)

# Use pytesseract to extract text from the image
extracted_text = pytesseract.image_to_string(image)
extracted_textThe extracted text from the image suggests a mathematical problem in Indonesian asking to simplify expressions involving square roots. Let's manually read the mathematical symbols from the image and proceed with solving them.

The tasks seem to be:

1. \( \frac{\sqrt{18}}{\sqrt{3}} \)
2. \( \frac{2\sqrt{20}}{\sqrt{5}} \)
3. \( \frac{8\sqrt{45}}{2\sqrt{3}} \) (the obscured problem)

### Let's simplify each expression step by step.

#### a. \( \frac{\sqrt{18}}{\sqrt{3}} \)

1. Simplify the fraction: \( \frac{\sqrt{18}}{\sqrt{3}} = \sqrt{\frac{18}{3}} \)
2. Calculate \( \frac{18}{3} = 6 \), so the expression becomes \( \sqrt{6} \).

#### b. \( \frac{2\sqrt{20}}{\sqrt{5}} \)

1. Simplify the fraction: \( \frac{2\sqrt{20}}{\sqrt{5}} = 2 \times \sqrt{\frac{20}{5}} \)
2. Calculate \( \frac{20}{5} = 4 \), so the expression becomes \( 2 \times \sqrt{4} = 2 \times 2 = 4 \).

#### d. \( \frac{8\sqrt{45}}{2\sqrt{3}} \)

1. Simplify the fraction: \( \frac{8\sqrt{45}}{2\sqrt{3}} = \frac{8}{2} \times \frac{\sqrt{45}}{\sqrt{3}} = 4 \times \sqrt{\frac{45}{3}} \)
2. Calculate \( \frac{45}{3} = 15 \), so the expression becomes \( 4 \times \sqrt{15} \).

### Solutions:

- a. \( \sqrt{6} \)
- b. \( 4 \)
- d. \( 4\sqrt{15} \)

Would you like more details or explanations? Here are 5 related questions to extend your understanding:

1. How do you simplify expressions involving square roots in general?
2. What are the properties of square roots that can be applied to division?
3. How can you rationalize the denominator in more complex square root expressions?
4. What are the common mistakes to avoid when simplifying square root fractions?
5. How do you handle square roots in multi-step algebraic expressions?

**Tip**: When simplifying square root expressions, always check if the numbers under the square root can be simplified further by finding perfect square factors.

Explore how to simplify square root fractions step-by-step with detailed solutions and explanations. Learn techniques for fraction simplification involving square roots, covering problems like \( \frac{\sqrt{18}}{\sqrt{3}}, \frac{2\sqrt{20}}{\sqrt{5}}, \) and more. Suitable for high school students.

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