Question

show 4 root 2 is an irrational number​

Answer 1

Answer:

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• To show 4√2 is irrational number.

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Let us assume that 4√2 is a rational number, in the form of p/q where 'p' and 'q' are integers and q≠0

So,

$= > 4 \sqrt{2 } = \frac{p}{q} \\ = > \sqrt{2 } = \frac{p}{4q}$

Since p/4q is in the form of p/q where 'p' and 'q' are Integers and q≠0.

Therefore:

p/4q is rational number

It means √2 will also be a rational number

But this contradicts. The fact that √2 is an irrational number.

Thus, we arrived in contraction.

Hence we proved √2 is an irrational number

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