Question

How do I know if a square root is irrational?

Answer 1

Hint:Irrational numbers are the numbers who are not exact; they are recurring after an interval and also non repeating numbers, so it’s impossible to find the square root of an irrational number and an exact value.

Complete step by step solution:
To find the square root of a number, you can use either factorization method or just by assumption or by vedic maths technique and many more examples are available.

The most appropriate and accurate and easy method is the factorization method, in this method you have to pair the factors obtained after factorization then all paired factors are multiplied together and put under the square root, for every pair the square degree on the pair is obsolete after solving it with root and after solving we are getting the final answer.

Here for any irrational number if you see the non repeating number in the root you can directly say that The given number is irrational.

For any number “\[x\]”
Let’s factors obtained are \[y,\,z,\,k\]

Here we assume that \[y,\,z\]are in pair and \[k\]is alone and is a irrational number, then we can say:
\[\sqrt x = y \times z \times \sqrt k \]
And \[x\]square root is irrational.

Note: You have to know the non repeating and non terminating numbers, for example a very famous non repeating number is pie, similarly you can find many more numbers just by finding its square root, and as you see the non repeating digits you can be sure with your number.