√2+√5 is irrational prove that

1.	√2+√5 is irrational prove that
Answer» Let us assume that √2+√5 is a rational number.A rational number can be written in the form of p/q where p,q are integers and q≠0√2+√5 = p/qOn squaring both sides we get,(√2+√5)² = (p/q)²√2²+√5²+2(√5)(√2) = p²/q²2+5+2√10 = p²/q²7+2√10 = p²/q²2√10 = p²/q² – 7√10 = (p²-7q²)/2qp,q are integers then (p²-7q²)/2q is a rational number.Then √10 is also a rational number.But this contradicts the fact that √10 is an irrational number.Our assumption is incorrect√2+√5 is an irrational number.Hence proved.

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