Задача 40819 ...

sova

2019-10-21 21:26:53

★

1) 7-2sqrt(10)=(sqrt(5))^2-2*sqrt(5)*sqrt(2)+(sqrt(2))^2=(sqrt(5)-sqrt(2))^2

sqrt(7-2sqrt(10))=sqrt((sqrt(5)-sqrt(2))^2)=|sqrt(5)-sqrt(2)|=sqrt(5)-sqrt(2)

sqrt(5)-sqrt(2)+sqrt(2)=sqrt(5)

sqrt(5)*2sqrt(5)=2*5=10

О т в е т. sqrt(10)


2)
16-6sqrt(7)=16-2*3*sqrt(7)=3^2-2*3*sqrt(7)+(sqrt(7))^2=(3-sqrt(7))^2

sqrt(16-6sqrt(7))=sqrt((3-sqrt(7))^2)=|3-sqrt(7)|=3-sqrt(7)

3-sqrt(7)+sqrt(7)=3

3*3=9

sqrt(9)=3

О т в е т. 3