3–√−9–√−23–√=
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43–√


−43–√


−3–√−3


3–√(1+3–√)




To solve the expression \( \sqrt{3} - \sqrt{9} - \sqrt{23} \), let's break it down step by step:

1. **Calculate each square root:**
   - \( \sqrt{3} \) is an irrational number, approximately 1.732.
   - \( \sqrt{9} = 3 \).
   - \( \sqrt{23} \) is also an irrational number, approximately 4.796.

2. **Substitute these values into the expression:**
   - \( \sqrt{3} - \sqrt{9} - \sqrt{23} \approx 1.732 - 3 - 4.796 \).

3. **Perform the operations:**
   - \( 1.732 - 3 = -1.268 \).
   - \( -1.268 - 4.796 = -6.064 \).

This value is negative and does not match any simple form that can be easily recognized. However, none of the provided answer options exactly match this calculation. Let's examine the given choices more closely:

1. \( \sqrt{43} \approx 6.557 \) (This is not correct because the original expression results in a negative number.)
2. \( -\sqrt{43} \approx -6.557 \) (This is approximately correct in magnitude but not exact.)
3. \( -\sqrt{3} - \sqrt{3} \) does not simplify in a way that matches the operations done.
4. \( \sqrt{3} \times (\sqrt{1} + \sqrt{3}) \) involves an additional multiplication that isn't relevant to the original expression.

Given this, the closest correct answer from the choices provided seems to be \( -\sqrt{43} \), as it approximates the negative result we calculated, although it's not exact.

### Would you like further details or have any questions?
  
Here are some related questions:
1. How can we simplify expressions involving square roots?
2. What are the properties of square roots of irrational numbers?
3. How do we handle subtraction involving irrational square roots?
4. What are the common methods to approximate square roots?
5. Can you explain how to simplify nested square root expressions?

**Tip:** Always consider the magnitude and sign of each term when dealing with square roots to ensure accuracy in solutions.

Learn how to solve the expression sqrt(3) - sqrt(9) - sqrt(23) with detailed step-by-step instructions. This problem involves operations with square roots and requires careful calculation and understanding of square root properties. Suitable for advanced high school students.

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