ÌâÄ¿ÄÚÈÝ
1£®¼ÆË㣨1£©£¨$\sqrt{48}$-$\sqrt{50}$+$\sqrt{75}}$£©£¨-$\sqrt{6}}$£©
£¨2£©$\sqrt{8}$-$\frac{1}{8}$$\sqrt{48}$-£¨$\frac{2}{3}$$\sqrt{4\frac{1}{2}}$-2$\sqrt{\frac{3}{4}}}$£©
£¨3£©£¨1+$\sqrt{2}}$£©2£¨1+$\sqrt{3}}$£©2£¨1-$\sqrt{2}}$£©2£¨1-$\sqrt{3}}$£©2
£¨4£©£¨$\sqrt{3}$-2$\sqrt{5}}$£©£¨$\sqrt{15}$+5£©-£¨$\sqrt{10}$-$\sqrt{2}}$£©2£®
·ÖÎö £¨1£©ÏȰѸ÷¶þ´Î¸ùʽ»¯¼òΪ×î¼ò¶þ´Î¸ùʽ£¬È»ºóºÏ²¢¼´¿É£»
£¨2£©ÏȰѸ÷¶þ´Î¸ùʽ»¯¼òΪ×î¼ò¶þ´Î¸ùʽ£¬È»ºóºÏ²¢¼´¿É£»
£¨3£©ÀûÓÃÆ½·½²î¹«Ê½¼ÆË㣻
£¨4£©ÀûÓó˷½¹«Ê½Õ¹¿ª£¬È»ºóºÏ²¢¼´¿É£®
½â´ð ½â£º£¨1£©Ôʽ=£¨4$\sqrt{3}$-5$\sqrt{2}$+5$\sqrt{3}$£©•£¨-$\sqrt{6}$£©
=£¨9$\sqrt{3}$-5$\sqrt{2}$£©•£¨-$\sqrt{6}$£©
=-27$\sqrt{2}$+10$\sqrt{3}$£»
£¨2£©Ôʽ=2$\sqrt{2}$-$\frac{\sqrt{3}}{2}$-$\sqrt{2}$+$\sqrt{3}$
=$\sqrt{2}$+$\frac{\sqrt{3}}{2}$£»
£¨3£©Ôʽ=[£¨1+$\sqrt{2}$£©£¨1-$\sqrt{2}$£©]2•[£¨1+$\sqrt{3}$£©£¨1-$\sqrt{3}$£©]2
=£¨1-2£©2•£¨1-3£©2
=1¡Á4
=4£»
£¨4£©Ôʽ=3$\sqrt{5}$+5$\sqrt{3}$-10$\sqrt{3}$-10$\sqrt{5}$-£¨10-4$\sqrt{5}$+2£©
=3$\sqrt{5}$+5$\sqrt{3}$-10$\sqrt{3}$-10$\sqrt{5}$-10+4$\sqrt{5}$-2
=-3$\sqrt{5}$-5$\sqrt{3}$-12£®
µãÆÀ ±¾Ì⿼²éÁ˶þ´Î¸ùʽµÄ»ìºÏÔËË㣺ÏȰѸ÷¶þ´Î¸ùʽ»¯¼òΪ×î¼ò¶þ´Î¸ùʽ£¬È»ºó½øÐжþ´Î¸ùʽµÄ³Ë³ýÔËË㣬Ôٺϲ¢¼´¿É£®