Question

prove that 3 + 2√5 is irrational
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Answer 1

Answer:

Step-by-step explanation:

Let us assume 3+25√ + is rational.

So we can write this number as

3+25√=ab ---- (1)

Here a and b are two co-prime number and b is not equal to zero.

Simplify the equation (1) subtract 3 both sides, we get

25√=ab−3

25√=a−3bb

Now divide by 2 we get

5√=a−3b2b

Here a and b are integer so a−3b2b is a rational number, so 5√ should be a rational number.

But 5√ is a irrational number, so it is contradict.

Therefore, 3+25√ is irrational number.

Answer 2

Answer:

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Step-by-step explanation:

3 + 2√5 = a/ b

2√5 =a/b -3

√5 =a-3b/2b

√5 is rational.

This contradicta the fact that √5 is irrational.

So our supposition is incorrect.

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