Question

сократите дробь:
$frac{ sqrt{50} - 2 sqrt{5} }{5 - sqrt{10} }$
упростите выражение:
$(9 - 2 sqrt{14} : ) : { :( sqrt{2} + sqrt{7} )}^{2}$

Answer 1

1.Сократить выражение:

$frac{sqrt{50} -2sqrt{5}}{5-sqrt{10}}\ \frac{5sqrt{2}-2sqrt{5}}{5-sqrt{10}}\ \frac{(5sqrt{2}-2sqrt{5})*(5+sqrt{10})}{15}\ \ frac{25sqrt{2}+5sqrt{20}-10sqrt{5}-2sqrt{50}}{15}\ \5sqrt{2^{2}*5}\5sqrt{2^2}sqrt{5}\5*2sqrt{5}\10sqrt{5}\ \frac{25sqrt{2}+10sqrt{5}-10sqrt{5}-2sqrt{50}}{15}\ \frac{25sqrt{2}-10sqrt{2}  }{15}\ \frac{15sqrt{2}}{15}\ \sqrt{2}$

2.Упростить выражение:

$(9-2sqrt{14})*(sqrt{2}+sqrt{7})^2\(9-2sqrt{14})*(2+2sqrt{14}+7)\(9-2sqrt{14})*(9+2sqrt{14})\9^2-(2sqrt{14})^2\81-4*14\81-56=25.$