Question

Упростите выражение......

Answer 1

(√10 - 1)(√10 +1)=10-1=9

$\frac{4-\sqrt{5} }{3+\sqrt{5} }=\frac{(4-\sqrt{5})(3-\sqrt{5})}{(3+\sqrt{5})(3-\sqrt{5} )}=\frac{12-4\sqrt{5}-3\sqrt{5}+5}{9-5} =\frac{17-7\sqrt{5} }{4}=0.25(17-7\sqrt{5})$

$\frac{\sqrt{3} }{\sqrt{3+\sqrt{2} } } =(\frac{\sqrt{3} }{\sqrt{3+\sqrt{2} } })^{2}=\frac{3}{3+\sqrt{2} } =\frac{3(3-\sqrt{2})}{(3+\sqrt{2})(3-\sqrt{2})} =\frac{9-3\sqrt{2} }{9-2}=\frac{9-\sqrt{2} }{7}$

$\frac{1}{1-\sqrt[4]{7} }=\frac{1+\sqrt[4]{7} }{(1-\sqrt[4]{7})(1+\sqrt[4]{7})}  =\frac{1+\sqrt[4]{7}}{1-\sqrt{7}} =\frac{(1+\sqrt[4]{7})(1+\sqrt{7}) }{(1-\sqrt{7})(1+\sqrt{7})} =\frac{1+\sqrt{7}+\sqrt[4]{7}+\sqrt[8]{7^{2}*7^{4}}}{1-7}=\\ \\ \frac{1+\sqrt{7}+\sqrt[4]{7}+\sqrt[8]{7^{8} } }{-6}=-\frac{8+\sqrt{7}+\sqrt[4]{7} }{6}$