Question

prove that √5-√3 is not rational

Answer 1

Answer:

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.

Answer 2

Answer:

How can someone prove that √5 - √3 is not a rational number? If √5 - √3 is rational then √5 - √3 = a/b for some integer a/b. Then (√5 - √3)^2 = a^2/b^2 for some integers a^2 and b^2. That is (√5 - √3)^2 is rational.

Step-by-step explanation:

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