Question

What is the simplest radical form of $\sqrt{115}$?

Answer 1

Hint: We solve this problem by taking out the possible perfect square out of the square root to get its simplest form. The simplest form is nothing but the representation of a given number making the value inside the square root it its least value.
We take the number 115 and represent it in the form of a product of one perfect square and some other number by using the prime factorisation method so that we can take out the perfect square out of square root to get the required answer.

Complete step by step solution:
We are asked to find the simplest radical form of $\sqrt{115}$
Let us assume that the required value as,
$\Rightarrow x=\sqrt{115}$
We know that the simplest radical form of a given number is the representation of a given number making the value inside the square root its least value by taking the perfect square out of the square root.
We know that, in order to represent the given number in simplest form we need to take the given number as the product of perfect square and some other number.
Let us use the prime factorisation method for the number 115.
Here, we can see that the number 115 is not divided by 2 and 3 so let us take the next prime number that is 5 then we get the number 115 as,
$\Rightarrow x=\sqrt{5\times 23}$
Here, we can see that the number 5 and 23 both are prime numbers so that we represent the number 115 as a product of 5 and 23.
We know that neither of 5 nor 23 are perfect squares so that we cannot take them out of the square root.
So, we can conclude that the simplest radical form of the given number $\sqrt{115}$ is in its simplest form.

Note: We are asked to find the simplest radical form of $\sqrt{115}$ but not the value of $\sqrt{115}$
So, we need to represent the number having the value inside the square root such that it cannot be represented as product of perfect square and some other number by taking out the possible perfect square out of square root.
But some students may do mistake finding the value of square root which is not the required answer.