Question

Prove that root 11 is irrational ​

Answer 1

√11

√9+√2

3√2

therefore it's irrational

Answer 2

Answer:

$\sqrt{11}$ is indeed irrational

Step-by-step explanation:

Firstly, what is irrational number?

An irrational number is a number that cannot be converted into fractions, and converted back.

And also, the decimal number that aren't repeating is also a irrational number.

For example :

$\frac{1}{3}$ is rational because :

It's decimal is repeating :

0.3333333

0.4085837693 is irrational because :

It cannot be converted into fractions.

Now, towards the question.

$\sqrt[11}$Is $\sqrt{11}$ irrational?

Firstly, solve $\sqrt{11}$.

$\sqrt{11}$ = 3.31662479036 ............ ( and so on )

The decimal is not repeating.

So it's irrational.

Secondly, you look into the decimal.

Can it be converted into fraction?

3.31662479036 ............ ( and so on )

AND SO ON.

Which means that the value behind is undetermined.

So therefore, converting $\sqrt{11}$ into fractions is not possible.

And therefore, $\sqrt{11}$ is irrational.

HOPE THIS ANSWER HELPED :)