Question

prove that 3+2root5 is irrational
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Answer 1

Answer:

Let take that 3 + 2root5 is a rational number.  

So we can write this number as  

3 + 2?5 = a/b  

Here a and b are two co prime number and b is not equal to 0

Subtract 3 both sides we get  

2root5 = a/b � 3

2root5 = (a-3b)/b

Now divide by 2 we get  

root5 = (a-3b)/2b

Here a and b are integer so (a-3b)/2b is a rational number so root5 should be a rational number But ?5 is a irrational number so it contradict the fact  

Hence result is 3 + 2root5 is a irrational number

Step-by-step explanation:

Answer 2

Let 3 + 2√5 be a rational number.

So,

3 + 2√5 = a/b

Here a and b are co prime numbers and b is not =0.

2√5 = a/b - 3

√5 = a/2b-3

Now,

Here a and b are integer.

Then a /2b-3 is a rational number so √5 should be a rational number.

But, √5 is a irrational number.

Hence, 3 + 2√5 is a irrational number.