[tex]( \sqrt{5} - \sqrt{7} )^2= \sqrt{5} ^2-2 \times \sqrt{5} \times \sqrt{7} + \sqrt{7} ^2=5-2 \sqrt{35} +7=12-2 \sqrt{35} \\ (2 \sqrt{3} +1)^2=(2 \sqrt{3} )^2+2 \times 2 \sqrt{3} \times 1+1^2=12+4 \sqrt{3} +1=13+4 \sqrt{3} \\ (3- \sqrt{5} )^2=3^2-2 \times 3 \times \sqrt{5} + \sqrt{5} ^2=9-6 \sqrt{5} +5=14-6 \sqrt{5} \\ (5 \sqrt{2} +3 \sqrt{5} )^2=(5 \sqrt{2} )^2+2 \times 5 \sqrt{2} \times 3 \sqrt{5} +(3 \sqrt{5} )^2= \\ =50+30 \sqrt{10} +45=95+30 \sqrt{10} [/tex]
