Question

Пожалуйста, помогите! Номер 136

Answer 1

а)

$2sqrt{20}-3sqrt{45}+3sqrt{80}-sqrt{125}=\\=2sqrt{4*5}-3sqrt{9*5}+3sqrt{16*5}-sqrt{25*5}=\\=2*2sqrt{5}-3*3sqrt{5}+3*4sqrt{5}-5sqrt{5}=\\=4sqrt{5}-9sqrt{5}+12sqrt{5}-5sqrt{5}=2sqrt{5}$

б)

$10sqrt{frac{2}{5}}-0,5sqrt{160}+3sqrt{1frac{1}{9}}=\\=10sqrt{frac{2*5}{5*5}}-0,5sqrt{16*10}+3sqrt{frac{10}{9}}=\\=10*frac{1}{5}*sqrt{10}-0,5*4*sqrt{10}+3*frac{1}{3}*sqrt{10}=\\=2sqrt{10}-2sqrt{10}+sqrt{10}= sqrt{10}$

в)

$(sqrt{15}-sqrt{6})^2+6sqrt{10}=\\=(sqrt{15})^2-2*sqrt{15}*sqrt{6}+(sqrt{6})^2+6sqrt{10}=\\=15-2sqrt{90}+6+6sqrt{10}=\\=21-2sqrt{9*10}+6sqrt{10}=\ \ =21-6sqrt{10}+6sqrt{10}=21$

г)

$(frac{3}{sqrt{3}}+frac{7}{sqrt{7}})*(sqrt{7}-sqrt{3})=\\=(frac{3*sqrt{3}}{sqrt{3}*sqrt{3}}+frac{7*sqrt{7}}{sqrt{7}*sqrt{7}})*(sqrt{7}-sqrt{3})=\\=(frac{3*sqrt{3}}{3}+frac{7*sqrt{7}}{7})*(sqrt{7}-sqrt{3})=\\=(sqrt{7}+sqrt{3})*(sqrt{7}-sqrt{3})=\\=(sqrt{7})^2-(sqrt{3})^2=7-3=4$