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प्रश्न
Examine, whether the following number are rational or irrational:
`(sqrt2+sqrt3)^2`
उत्तर
Let `x=(sqrt2+sqrt3)^2`be rational number
Using the formula (a + b)2 = a2 + b2 + 2ab
`rArrx=(sqrt2)^2+(sqrt3)^2+2(sqrt2)(sqrt3)`
`rArrx=2+3+2sqrt6`
`rArrx=5+2sqrt6`
`rArr(x-5)/2=sqrt6`
`rArr(x-5)/2` is a rational number
`rArrsqrt6` is a rational number
But we know that `sqrt6` is an irrational number
So, we arrive at a contradiction
So `(sqrt2+sqrt3)^2` is an irrational number.
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