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Prove That root 5 + root 2 is irrational
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Given that to prove √5+√2=Irrational
Now we'll assume that √5+√2 is Rational
As we know a rational number can be written in the form of p/q so
√2+√5=p/q
On squaring both sides we get
(√2+√5)²=(p/q)²
2+5+2√10=p²/q²
2√10=p²/q²-7
√10=(p²-7q²)/2q
if p/q is rational then (p²-7q²)/2q is also rational I contradics that √10 is also rational but we know √10 is irrational this means we are wrong that √2+√5 is rational
it clearly means √2+√5 is irrational
Hence proved
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