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Question

Prove that 2+5 is irrational number


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Solution

Solve for the required proof:

Let us assume 2+5 is not a irrational number, that is 2+5 is a rational number

So 2+5 can be expressed as pq where p,q and q0

2+5=pq2+52=pq22+210+5=pq2a+b2=a2+b2+2ab210=pq2-710=p2-7q22q2

Since, p,q and q0, then p2-7q22q2 must be a rational number.

But 10 is irrational .

Hence contradiction

So our assumption 2+5 is a rational number is incorrect

Therefore 2+5 is a irrational number.

Hence proved


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