Prove that √n is not a …

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Prove that √n is not a rational number.

Posted by Divanjyoti Deka 4 years, 3 months ago

CBSE > Class 09 > Mathematics

2 answers

Yogita Ingle 4 years, 3 months ago

If n is not a perfect square then is irrational
Let on the contrary say it is rational .

Then

where p and q are coprime integers.
so n =p²/q²

p² =nq²

This shows p divides q

which is a contradiction.

Hence is irrational if n is not a perfect square.

1Thank You

Malhar Mv 4 years, 3 months ago

We have to prove that √n is not a rational number, if n is not a perfect square. Ex: Let we take the number is √5 Here 5 is not a perfect square. Proof: ... Thus p and q has a common factor 5.

1Thank You

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CBSE > Class 09 > Mathematics