https://file.aiquickdraw.com/mathbot/file/1726192712611bwrwmqra.jpg

The image contains a mathematical expression that needs to be solved. The question appears to be:

\[
\left( \sqrt{2} - \sqrt{3} \right)^2
\]

The possible answers provided are:

A. \( 5 - 2\sqrt{6} \)  
B. \( 5 - \sqrt{6} \)  
C. \( 1 - 2\sqrt{6} \)  
D. \( 1 - \sqrt{2} \)  
E. 1

Let's expand the given expression and simplify it:

\[
\left( \sqrt{2} - \sqrt{3} \right)^2 = \left( \sqrt{2} \right)^2 - 2\left( \sqrt{2} \times \sqrt{3} \right) + \left( \sqrt{3} \right)^2
\]

First, calculate each term:

1. \( \left( \sqrt{2} \right)^2 = 2 \)
2. \( \left( \sqrt{3} \right)^2 = 3 \)
3. \( -2 \times \sqrt{2} \times \sqrt{3} = -2 \times \sqrt{6} \)

Thus, the expanded form is:

\[
2 + 3 - 2\sqrt{6} = 5 - 2\sqrt{6}
\]

Therefore, the correct answer is **A**.

Would you like any further details or clarification on this solution?

Here are 5 related questions:
1. How do you expand binomials like \( (a - b)^2 \)?
2. What is the rule for multiplying square roots, like \( \sqrt{2} \times \sqrt{3} \)?
3. Can you apply the same steps for \( (\sqrt{5} + \sqrt{7})^2 \)?
4. How does simplifying surds (like \( \sqrt{6} \)) work in general?
5. Why is the middle term \( -2 \times \sqrt{2} \times \sqrt{3} \) rather than something else?

**Tip:** Always remember to apply the distributive property carefully when squaring binomials involving roots.

(√2 - √3)^2 = ?
A. 5 - 2√6
B. 5 - √6
C. 1 - 2√6
D. 1 - √2
E. 1

Learn how to simplify the expression (√2 - √3)^2 with a detailed step-by-step solution. This problem covers key algebraic concepts like binomial expansion, radicals, and simplifying square roots. Suitable for students in Grades 9-11.

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