Rohan claims √2 can be written as a fraction p/q in lowest terms. Using the standard proof, what contradiction arises?

Question

Accepted Answer

Both p and q turn out to be even, contradicting lowest terms. Assuming √2 = p/q (coprime) leads to p^2 = 2q^2, so p is even, then q is even too. Both even contradicts coprime, proving √2 is irrational.

Rohan claims $2$ can be written as a fraction $\frac{p}{q}$ in lowest terms.
Using the standard proof, what contradiction arises?

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More Class 10 Irrational Numbers practice

Rohan claims 2​ can be written as a fraction qp​ in lowest terms.Using the standard proof, what contradiction arises?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Irrational Numbers practice

Rohan claims $2$ can be written as a fraction $\frac{p}{q}$ in lowest terms.
Using the standard proof, what contradiction arises?