RationalRick
{ Matematikus }
megoldása
1 éve
`856.`
`a)`
`sqrt(2)+sqrt(8)`
`sqrt(2)+sqrt(2^3)`
`sqrt(2)+2sqrt(2)=3sqrt(2)`
`b)`
`sqrt(3)+sqrt(12)+sqrt(27)`
`sqrt(3)+sqrt(2^2*3)+sqrt(3^3)`
`sqrt(3)+2sqrt(3)+3sqrt(3)=6sqrt(3)`
`c)`
`4sqrt(2)+3sqrt(18)-sqrt(50)`
`4sqrt(2)+3sqrt(2*3^2)-sqrt(2*5^2)`
`4sqrt(2)+3*3sqrt(2)-5sqrt(2)=8sqrt(2)`
`d)`
`5sqrt(3)+sqrt(75)-1/2sqrt(147)`
`5sqrt(3)+sqrt(3*5^2)-1/2*sqrt(3*7^2)`
`5sqrt(3)+5sqrt(3)-1/2*7sqrt(3)=6.5sqrt(3)`
`e)`
`5sqrt(4x)+4sqrt(x)+sqrt(9x)`
`5sqrt(2^2x)+4sqrt(x)+sqrt(3^2x)`
`5*2sqrt(x)+4sqrt(x)+3sqrt(x)=11sqrt(x)`
`f)`
`2sqrt(45)+sqrt(20)-3sqrt(80)`
`2sqrt(3^2*5)+sqrt(2^2*5)-3sqrt(2^4*5)`
`2*3sqrt(5)+2sqrt(5)-3*4sqrt(5)`
`6sqrt(5)+2sqrt(5)-12sqrt(5)=-4sqrt(5)`
`g)`
`3sqrt(2b)+sqrt(18b)-sqrt(8b)+2sqrt(50b)`
`3sqrt(2b)+sqrt(2*3^2)-sqrt(2^3)+2sqrt(2*5^2)`
`3sqrt(2b)+3sqrt(2b)-2sqrt(2b)+2*5sqrt(2b)`
`3sqrt(2b)+3sqrt(2b)-2sqrt(2b)+10sqrt(2b)=14sqrt(2b)`
`857`
`a)`
`(sqrt(2)+3sqrt(8)-sqrt(50))*2sqrt(2)`
`(sqrt(2)+3sqrt(2^3)-sqrt(2*5^2))*2sqrt(2)`
`(sqrt(2)+2*3sqrt(2)-5sqrt(2))*2sqrt(2)`
`2sqrt(2)*2sqrt(2)=8`
`b)`
`(2sqrt(3)+sqrt(27)-sqrt(12))*5sqrt(3)`
`(2sqrt(3)+sqrt(3^3)-sqrt(2^2*3))*5sqrt(3)`
`(2sqrt(3)+3sqrt(3)-2sqrt(3))*5sqrt(3)`
`3sqrt(3)*5sqrt(3)=45`
`c)`
`(sqrt(7)+sqrt(2))(sqrt(7)-sqrt(2))`
`(sqrt(7))^2-(sqrt(2))^2`
`7-2=5`
`d)`
`(sqrt(8)+sqrt(3))(sqrt(8)-sqrt(3))`
`(sqrt(8))^2-(sqrt(3))^2`
`8-3=5`
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