Question

simplify
$(2 \sqrt{2 - 5) {}^{2} } + (3 \sqrt{2 + \sqrt{3) {}^{2} } } - ( \sqrt{2 - 1) {}^{2} }$

Answer 1

The squares are not written correctly. I am assuming you wanted the following.
${( \: 2 \sqrt{2 - 5} \: ) }^{2} + { ( \: 3 \sqrt{2 + \sqrt{3} } \: \: )}^{2} - {( \: \sqrt{2 - 1} \: )}^{2} \\ \\ = 4 {(\sqrt{ - 3} \: ) }^{2} + 9{ ( \sqrt{2 + \sqrt{3} } \: \: )}^{2} - {( \: \sqrt{1} \: )}^{2} \\ \\ = 4 \times ( - 3) + 9(2 + \sqrt{3} \: ) - 1 \\ \\ = - 12 + 9 \times 2 + 9 \times \sqrt{3} - 1 \\ \\ = - 12 + 18 - 1 + 9 \sqrt{3} \\ \\ = 5 + 9 \sqrt{3}$