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.