\(g)\sqrt{\left(\sqrt{5}-2\right)^2}+\sqrt{14-6\sqrt{5}}\)
\(=|\sqrt{5}-2|+\sqrt{9-6\sqrt{5}+5}\)
\(=\sqrt{5}-2+\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(=\sqrt{5}-2+|3-\sqrt{5}|\)
\(=\sqrt{5}-2+3-\sqrt{5}\)
​\(=1\)
\(h)\sqrt{4-2\sqrt{3}}+\sqrt{\left(3-\sqrt{3}\right)^2\)
\(=\sqrt{3-2\sqrt{3}+1}+|3-\sqrt{3}|\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}+3-\sqrt{3}\)
\(=|\sqrt{3}-1|+3-\sqrt{3}\)
\(=\sqrt{3}-1+3-\sqrt{3}\)
\(=2\)
\(i)\sqrt{\left(2-\sqrt{7}\right)^2}+\sqrt{8+2\sqrt{7}}\)
\(=|2-\sqrt{7}|+\sqrt{7+2\sqrt{7}+1}\)
\(=\sqrt{7}-2+\sqrt{\left(\sqrt{7}+1\right)^2}\)
\(=\sqrt{7}-2+|\sqrt{7}+1|\)
\(=\sqrt{7}-2+\sqrt{7}+1\)
\(=2\sqrt{7}-1\)
\(j)\sqrt{11-4\sqrt{7}}-\sqrt{\left(\sqrt{7}-3\right)^2}\)
\(=\sqrt{4-4\sqrt{7}+7}-|\sqrt{7}-3|\)
\(=\sqrt{\left(2-\sqrt{7}\right)^2}+\sqrt{7}-3\)
\(=|2-\sqrt{7}|+\sqrt{7}-3\)
\(=\sqrt{7}-2+\sqrt{7}-3\)
\(=2\sqrt{7}-5\)
\(k)\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{7-4\sqrt{3}}\)
\(=|\sqrt{3}-1|+\sqrt{4-4\sqrt{3}+3}\)
\(=\sqrt{3}-1+\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=\sqrt{3}-1+|2-\sqrt{3}|\)
\(=\sqrt{3}-1+2-\sqrt{3}\)
\(=1\)
\(l)\sqrt{\left(\sqrt{5}+2\right)^2}-\sqrt{14-6\sqrt{5}}\)
\(=|\sqrt{5}+2|-\sqrt{9-6\sqrt{5}+5}\)
\(=\sqrt{5}+2-\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(=\sqrt{5}+2-|3-\sqrt{5}|\)
\(=\sqrt{5}+2-3+\sqrt{5}\)
\(=2\sqrt{5}-1\)
\(m)\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\)
\(=|2-\sqrt{5}|+\sqrt{9-6\sqrt{5}+5}\)
\(=\sqrt{5}-2+\sqrt{\left(3-\sqrt{5}\right)^2}\)
\(=\sqrt{5}-2+|3-\sqrt{5}|\)
\(=\sqrt{5}-2+3-\sqrt{5}\)
\(=1\)
\(n)\sqrt{\left(2+\sqrt{5}\right)^2}+\sqrt{21-8\sqrt{5}}\)
\(=|2+\sqrt{5}|+\sqrt{16-8\sqrt{5}+5}\)
\(=2+\sqrt{5}+\sqrt{\left(4-\sqrt{5}\right)^2}\)
\(=2+\sqrt{5}+|4-\sqrt{5}|\)
\(=2+\sqrt{5}+4-\sqrt{5}\)
\(=6\)