Prove that 3+2√5 is irrational number

1.	Prove that 3+2√5 is irrational number
Answer» Let take that 3 + 2√5 is a rational number.So we can write this number as3 + 2√5 = a/bHere a and b are two co prime number and b is not equal to 0Subtract 3 both sides we get2√5 = a/b – 32√5 = (a-3b)/bNow divide by 2 we get√5 = (a-3b)/2bHere a and b are integer so (a-3b)/2b is a rational number so √5 should be a rational number But √5 is a irrational number so it contradict the factHence result is 3 + 2√5 is a irrational number Let 3+2√5 be a rational no.3+√5=a/b (a & b are co-prime no.)√5=a-3b/b (we know that √5 is a irrational no)This contradict the fact that 3+√5 is a irrational no.

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