Question

Prove that (√5 - √3) is not a rational number.​

Answer 1

Answer:

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Answer 2

Answer:

First of all, we have to prove that √5 is an irrational number. By similar procedure, it can also be proved that √3 is also an irrational number.

After proving, suppose (let us assume) that √5 - √3 is rational number (say, r)

Then, √5 - √3 = r (r ≠ 0)  

Or, √5 = r + √3  

As "r" is rational, so (r+√3) is also rational , and hence √5 is also rational, since (r+√3) is equal to √5.  

But, this contradicts our assumption since we know √5 is irrational number.  

Therefore, √5 - √3 is an irrational number.

Step-by-step explanation:

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