Question

Prove 5-7root 3 is irrational

Answer 1

Answer:

5-3/7root is rational number do p and q are co prime such that 5-3/7root3=p/q

5-3=p/q 7 root 3 2p/7q=root 3

where as 2p/7q is a rational and root 3 is aorrational number

therefore 5-3/7root 3 is a irrational number

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Answer 2

TO PROVE ] 5-7√3 is irrational

Let 5-7√3 is rational

5-7√3 can be expressed in the form of P/q

5-7√3 = p/q

-7√3 = p/q - 5q/q

7√3 = -(p/q + 5q/q)

√3 = -(p/7q + 5q/7q)

→ -(p/7q + 5q/7q) should be rational.

Therefore√3 should also be rational .

BUT √3 is irrational

♦Therefore our supposition is wrong

→Hence 5-7√3 is irrational.

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