Question

What is the square root of $$31$$ in simplest form?

Answer 1

Hint:The number given in the question has to be solved down to its simplest form possible in terms of a radical. The simplest form for the given number (or radical) will be found out by finding out if any one of the factors of $31$ is a perfect square the number will come out of the root sign and the remaining number will be the radical form. If the number does not have any perfect squares as its factor we can say the number is already in its simplest form.

Complete step by step answer:
The simplest form for the given number will be found out by finding out if any one of the factors of $31$ is a perfect square the number will come out of the root sign and the remaining number will be the simplest form. We now factorize $31$.

The number itself is already a prime number because it has no factors except $1$ and itself. Since no factor is a perfect square we can say that the number $\sqrt{31}$ Is already in its simplest radical form. The solution of it in the decimal form can be found out by the long division method, the solution of which we get $5.568$.

Note: The numbers under the root sign which cannot be broken further into simpler roots are called to be as the surds or radicals. The surd or radical can have any $nth$root , it can be square root or it can be cube root. The example of a surd is $\sqrt{2}$.