Question

why is (-√0.4) a irrational number?​

Answer 1

Since the number is non terminating and non repeating therefore it is irrational number.

Answer 2

We have to write -√0.4 in fractional form

$= > - \sqrt{0.4 }$

$= > - \sqrt{ \frac{4}{10} }$

$= > \frac{2}{ \sqrt{10} }$

As √10 is irrational, then so will be -2/√10, because a rational number divided by an irrational number gives irrational.

Thus we can say that -√0.4 is irrational.

Or, let me prefer you another method.

Assume that -√0.4 is rational, and let it be x where x is a rational number.

$= > x = - \sqrt{ 0.4}$

$= > x = - \frac{2}{ \sqrt{10} }$

$= > \sqrt{10} = - \frac{2}{x}$

A contradiction occurs at the last step as it seems that √10 can be written as a fraction, but it's actually irrational.

This contradiction breaks our earlier assumption that -√0.4 is rational.

Hence we can also say that -√0.4 is irrational.

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