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=Question 1

=Question 2

=Question 3

 

Question 2. Prove that 3 + 2√5 is irrational.

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Question 2. Prove that 3 + 2√5 is irrational.

Answer:
Let take that 3 + 2√5 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
2√5 = a/b – 3
2√5 = (a-3b)/b
Now divide by 2 we get
√5 = (a-3b)/2b
Here 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 fact
Hence result is 3 + 2√5 is a irrational number



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Question 2. Prove that 3 + 2?5 is irrational.

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