Question

prove that 7 /5 root 2 is not rational number given that root 2 is irrational

Answer 1

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Answer 2

Answer:

The proof is below.

Step-by-step explanation:

We have to prove that $\frac{7}{5\sqrt2}$ is irrational number.

Let us assume that $\frac{7}{5\sqrt2}$ is a rational number.

As rational number are the number which can be expressed in the form of $\frac{p}{q}$ where q is not equals to 0.

∴ $\frac{7}{5\sqrt2}=\frac{p}{q}$

⇒  $\frac{7q}{5p}=\sqrt2$

As $\frac{7q}{5p}$ is a rational number

⇒ $\sqrt2$ is also rational

which is contradiction because given $\sqrt2$ is irrational.

Hence, our supposition is wrong

$\frac{7}{5\sqrt2}$ is irrational number.