\( \displaystyle \sqrt{27}+ 2\sqrt{3}=\sqrt{3^2\times 3}+ 2\sqrt{3} \)
\( \displaystyle =3\sqrt{3}+ 2\sqrt{3}=5\sqrt{3} \) \( \displaystyle \sqrt{8}+ \sqrt{18}- \sqrt{2}=\sqrt{2^2\times 2}+ \sqrt{2\times 3^2}-\sqrt{2} \)
\( \displaystyle =2\sqrt{2}+ 3\sqrt{2}-\sqrt{2}=4\sqrt{2} \) \( \displaystyle \sqrt{50}- \sqrt{18}=\sqrt{2\times 5^2}-\sqrt{2\times 3^2} \)
\( \displaystyle =5\sqrt{2}-3\sqrt{2}=2\sqrt{2} \) \( \displaystyle \sqrt{3}- \sqrt{12}=\sqrt{3}-\sqrt{2^2\times 3} \)
\( \displaystyle =\sqrt{3}-2\sqrt{3}=-\sqrt{3} \) \( \displaystyle 5\sqrt{3}- \sqrt{12}=5\sqrt{3}- \sqrt{2^2\times 3} \)
\( \displaystyle =5\sqrt{3}- 2\sqrt{3}=3\sqrt{3} \) \( \displaystyle \sqrt{32}- \sqrt{18}=\sqrt{2\times 4^2}- \sqrt{2\times 3^2} \)
\( \displaystyle =4\sqrt{2}- 3\sqrt{2}=\sqrt{2} \) \( \displaystyle \sqrt{18}+ \sqrt{50}-\sqrt{8}=\sqrt{2\times 3^2}+ \sqrt{2 \times 5^2}- \sqrt{2^2\times 2} \)
\( \displaystyle =3\sqrt{2}+ 5\sqrt{2}- 2\sqrt{2}=6\sqrt{2} \) \( \displaystyle \sqrt{48}- 5\sqrt{3}+ \sqrt{27}=\sqrt{3\times 4^2}-5\sqrt{3}+ \sqrt{3^2\times 3} \)
\( \displaystyle =4\sqrt{3}-5\sqrt{3}+ 3\sqrt{3}=2\sqrt{3} \) \( \displaystyle 5\sqrt{3}+ \sqrt{12}=5\sqrt{3}+ \sqrt{2^2\times 3} \)
\( \displaystyle =5\sqrt{3}+ 2\sqrt{3}=7\sqrt{3} \) \( \displaystyle 5\sqrt{7}- \sqrt{28}=5\sqrt{7}- \sqrt{2^2\times 7} \)
\( \displaystyle =5\sqrt{7}- 2\sqrt{7}=3\sqrt{7} \) →解説を隠す←