Prove that 3+√5 is irrational ?

1.	Prove that 3+√5 is irrational ?
Answer» Let √3+√5 be any rational number xx=√3+√5squaring both sides x²=(√3+√5)²x²=3+5+2√15x²=8+2√15x²-8=2√15(x²-8)/2=√15as x is a rational number so x²is also a rational number, 8 and 2 are rational nos. , so √15 must also be a rational number as quotient of two rational numbers is rational but, √15 is an irrational number so we arrive at a contradiction tthis shows that our supposition was wrong so √3+√5 is not a rational number

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