यदि 'a' तथा 'b' दोनों परिमेय संख्याये हो तो निम्नलिखित में 'a' तथा 'b' का मान ज्ञात कीजिए :
`(5+2sqrt3)/(7+4sqrt3)=a+bsqrt3`

Explanation

हर के परिमेयकारी गुणक से अंश तथा हर को गुणा करने पर
`(5+2sqrt3)/(7+4sqrt3)=(5+2sqrt3)/(7+4sqrt3)xx(7-4sqrt3)/(7-4sqrt3)=((5+2sqrt3)(7-4sqrt3))/((7+4sqrt3)(7-4sqrt3))`
`implies(5+2sqrt3)/(7+4sqrt3)=(5xx7-5xx4sqrt3+2sqrt3xx7-2sqrt3xx4sqrt3)/(7^(2)-(4sqrt3)^(2))`
`implies(5+2sqrt3)/(7+4sqrt3)=(35-20sqrt3+14sqrt3-8sqrt3xx3)/(49-16xx(sqrt3)^(2))`
`implies(5+2sqrt3)/(7+4sqrt3)=(35-(20-14)sqrt3-8sqrt3xx3)/(49-16xx3)`
`implies(5+2sqrt3)/(7+4sqrt3)=(35-(20-14)sqrt3-8sqrt3xx3)/(49-48)=(35-6sqrt3-24)/(49-48)=11-6sqrt3`
`:.(5+2sqrt3)/(7+4sqrt3)=a+bsqrt3`
`impliesa+bsqrt3=11-6sqrt3`
`impliesa+bsqrt3=11+(-6)sqrt3`
`impliesa=11" तथा "b=-6`