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`(1)/(sqrt(2)+sqrt(3)+sqrt(10))` के हर का परिमेयीकरण कीजिए ।

Answer» यहाँ `" " (1)/(sqrt(2)+sqrt(3)+sqrt(10))=(1)/((sqrt(2)+sqrt(3))+sqrt(10))`
अब,
`(1)/((sqrt(2)+sqrt(3))+sqrt(10))xx((sqrt(2)+sqrt(3))-sqrt(10))/((sqrt(2)+sqrt(3)))=((sqrt(2)+sqrt(3))-sqrt(10))/((sqrt(2)+sqrt(3))^(2)-(sqrt(10))^(2))`
`=(sqrt(2)+sqrt(3)-sqrt(10))/(2+3+2sqrt(2)sqrt(3)-10)=(sqrt(2)+sqrt(3)-sqrt(10))/(2sqrt(6)-5)`
पुनः हर का परिमेयीकरण करने पर
`(1)/(sqrt(2)+sqrt(3)+sqrt(10))=(sqrt(2)+sqrt(3)-sqrt(10))/(2sqrt(6)-5)xx(2sqrt(6)+5)/(2sqrt(6)+5)`
`=((sqrt(2)+sqrt(3)-sqrt(10))(2sqrt(6)+5))/((2sqrt(6))^(2)-(5)^(2))=(2sqrt(12)+5sqrt(2)+2sqrt(18)+5sqrt(3)-2sqrt(60)-5sqrt(10))/(24-25)`
`=(2sqrt(2xx2xx3)+5sqrt(2)+2sqrt(3xx3xx2)+5sqrt(3)-2sqrt(2xx2xx3xx5)-5sqrt(2xx5))/(-1)`
`=-2(2^(2)xx3)^(1//2)-5sqrt(2)-2(3^(2)xx2)^(1//2)-5sqrt(3)+2(2^(2)xx3xx5)^(1//2)+5(2xx5)^(1//2)`
`=-4sqrt(3)-5sqrt(2)-6sqrt(2)-5sqrt(3)+4sqrt(15)+5sqrt(10)=-11sqrt(2)-9sqrt(3)+5sqrt(10)+4sqrt(15)`


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