https://file.aiquickdraw.com/mathbot/file/1726354117100hmrc09y5.jpg

The image contains a math problem written in Japanese. From what I can transcribe:

It appears to be asking the following:

**Problem Translation:**

When the decimal part of \(\sqrt{10} - 3\) is represented by \(a\), find the value of \(a^2 + 5a\).

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### Let's break it down:

1. First, calculate \(\sqrt{10}\).
   \[
   \sqrt{10} \approx 3.1623
   \]
2. Then, find \(\sqrt{10} - 3\):
   \[
   \sqrt{10} - 3 \approx 3.1623 - 3 = 0.1623
   \]
   So, \(a = 0.1623\).
   
3. Now, we need to calculate \(a^2 + 5a\):
   \[
   a^2 + 5a = (0.1623)^2 + 5(0.1623)
   \]

Let's compute this.

\[
a^2 = 0.1623^2 \approx 0.02634
\]
\[
5a = 5 \times 0.1623 = 0.8115
\]
\[
a^2 + 5a \approx 0.02634 + 0.8115 = 0.83784
\]

So, the value of \(a^2 + 5a \approx 0.8378\).

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Would you like any further details or explanation? Here are some related questions you could explore:

1. What is the general form of expressions like \(a^2 + 5a\)?
2. How can you approximate square roots more accurately?
3. What are other ways to solve quadratic equations like this?
4. How does the concept of decimal parts factor into more advanced math?
5. What role does \( \sqrt{10} \) play in geometry or trigonometry?

**Tip**: Always remember to retain at least four decimal places when calculating intermediate values for accuracy.

When the decimal part of √10 - 3 is represented by a, find the value of a^2 + 5a.

Learn how to calculate the value of a^2 + 5a where 'a' represents the decimal part of √10 - 3. This detailed step-by-step solution involves key algebraic concepts and decimal approximation techniques, suitable for students in Grades 7-9.

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