Question

prove 5√2 is irrational​

Answer 1

Answer:

let 5√2 be a rational no. so, it can be represented in the form of a/b where a and b both are co-prime

5√2= a/b

√2= a/5b

since 5, a and b are integers, a/5b is rational, and so √2 is rational.

but this contradicts the fact that √2 is irrational.

so, we conclude that 5√2 is irrational.

Answer 2

Assume that 5√2 is rational

Then,

5√2 = a/b {here , a and b are co- prime

and b≠ 0}

√2 = a/5b

a/5b are rational.

But, we know that √2 is irrational.

Therefore, our assumption is wrong that 5√2 is rational.

So, 5√2 is irrational.

Hence proved.

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