2) Calculate \( \mathrm{A} \times \mathrm{B} \) then deduce that \( \sqrt{A \times B} \) is in the form of \( \mathrm{a} \sqrt{2} \) where a is a natural number. 3) Calculate \( \mathrm{A}^{2}-\mathrm{B}^{2} \).

When dealing with the product \( \mathrm{A} \times \mathrm{B} \), it's helpful to think of \( \mathrm{A} \) and \( \mathrm{B} \) as special numerical forms, perhaps something like \( a + b\sqrt{2} \) and \( c + d\sqrt{2} \). When you multiply them out, you’ll get terms that can be simplified to find the common factors, ultimately showing that \( \sqrt{A \times B} = a\sqrt{2} \), where \( a \) will be derived from the coefficients after simplifying. When calculating \( \mathrm{A}^2 - \mathrm{B}^2 \), remember that this is a classic difference of squares. You can express it as \( (A - B)(A + B) \). If you substitute your earlier expressions for \( \mathrm{A} \) and \( \mathrm{B} \), the result will combine the constants and the square roots beautifully, often yielding a clear representation of how \( A \) and \( B \) relate to one another through their roots and coefficients. Enjoy simplifying those expressions!