\(a,\sqrt{7-2\sqrt{6}}\\ =\sqrt{6-2\sqrt{6}.1+1}\\ =\sqrt{\left(\sqrt{6}-1\right)^2}\\ =\sqrt{6}-1\\ b,\sqrt{8-2\sqrt{7}}\\ =\sqrt{7-2.\sqrt{7}.1+1}\\ =\sqrt{\left(\sqrt{7}-1\right)^2}\\ =\sqrt{7}-1\\ c,\sqrt{7+4\sqrt{3}}\\ =\sqrt{2^2+2.2\sqrt{3}+\sqrt{3^2}}\\ =\sqrt{\left(2+\sqrt{3}\right)^2}\\ =2+\sqrt{3}\\ d,\sqrt{9-4\sqrt{5}}\\ =\sqrt{4^2-2.2.\sqrt{5}+\sqrt{5^2}}\\ =\sqrt{\left(4-\sqrt{5}\right)^2}\\ =4-\sqrt{5}\)
\(e,\sqrt{13-4\sqrt{3}}\\ =\sqrt{\left(2\sqrt{3}\right)^2-2.2\sqrt{3}.1+1^2}\\ =\sqrt{\left(2\sqrt{3}-1\right)^2}\\ =2\sqrt{3}-1\\ f,\sqrt{23+8\sqrt{7}}\\ =\sqrt{4^2+2.4\sqrt{7}+\sqrt{7^2}}\\ =\sqrt{\left(4+\sqrt{7}\right)^2}\\ =4+\sqrt{7}\\ g,\sqrt{4-2\sqrt{3}}-\sqrt{3}\\ =\sqrt{\sqrt{3^2}-2\sqrt{3}.1+1^2}-\sqrt{3}\\ =\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\\ =\sqrt{3}-1-\sqrt{3}\\ =-1\)
