Question

Calculati: $x^{2} \sqrt{(2- \sqrt{3} ) ^{2} } + x^{2} \sqrt{(3-2 \sqrt{3}) ^{2} } - x^{2} \sqrt{(1- \sqrt{3} ) ^{2} }$

Answer 1

$\sqrt{(2- \sqrt{3}) ^{2} }=|2- \sqrt{3}|=2- \sqrt{3} \\ \sqrt{(3- 2\sqrt{3})^{2} }=|3- 2\sqrt{3}|=2 \sqrt{3}-3 \\ \sqrt{(1- \sqrt{3})^{2} }=|1- \sqrt{3}|= \sqrt{3}-1$
Inlocuiesc:

$x^{2} \sqrt{(2- \sqrt{3})^{2} } + x^{2} \sqrt{(3- 2\sqrt{2}) ^{2} } - x^{2} \sqrt{(1- \sqrt{3}) ^{2} } = \\ = x^{2} (2- \sqrt{3})+ x^{2} (2 \sqrt{2}-3 )- x^{2} ( \sqrt{3}-1)= \\ = x^{2} (2- \sqrt{3}+ 2\sqrt{2}-3- \sqrt{3}+1)= \\ = x^{2} *0= \\ =0.$