Question

Найти значения выражений с кв. корнями. С решением

Answer 1

$1)(sqrt{45}+sqrt{5})*sqrt{5}=sqrt{45*5}+sqrt{5*5}=sqrt{225}+sqrt{25}=15+5=20$

$2)sqrt{13*18}*sqrt{26}=sqrt{13*18*26}=sqrt{13*2*9*2*13}=sqrt{13^2}*sqrt{9}*sqrt{2^2}=$

 $=13*3*2=78$

$3)frac{sqrt{8}*sqrt{192}}{sqrt{24}}=frac{sqrt{8}*sqrt{192}}{sqrt{8}*sqrt{3}}=sqrt{frac{192}{3}}=sqrt{64}=8$

$4)sqrt{42*75*14}=sqrt{14*3*25*3*14}=sqrt{14^2}*sqrt{3^2}*sqrt{25}=14*3*5=210$

$5)10sqrt{7}*2sqrt{6}*sqrt{42}=10*2*sqrt{7*6}*sqrt{42}=20*sqrt{42}*sqrt{42}=20*42=840$

$6)sqrt{7*3^4}*sqrt{7*2^2}=sqrt{7*3^4*7*2^2}=sqrt{7*7}*sqrt{3^4}* sqrt{2^2}=$

  $=7*3^2*2=7*9*2=126$

$7)frac{200}{(5sqrt{2})^2}=frac{200}{5^2*(sqrt{2})^2}=frac{200}{25*2}=frac{200}{50}=4$

$8)sqrt{(-29)^2}=sqrt{29^2}=29$

$9)frac{1}{5+sqrt{23}}}+frac{1}{5-sqrt{23}}}=frac{5-sqrt{23}+5+sqrt{23}}{5^2-(sqrt{23})^2}}=frac{5+5}{25-23}=frac{10}{2}=5$

Answer 2

Ответ: во вложении Объяснение: