Question

What is the simplest radical form of \[14\]?

Answer 1

Hint: In the above problem, we are given a number that is 14 which is a real number and we are asked to find its radical form. Before solving such a question, we should know about the radical form and the real numbers as the radical expression or those expressions which contain square root, cubical root or fractional in their expressions and the real numbers are the numbers which can be negative or positive or decimal. In this problem, we are given by the real number, which can be broken down into small factors to find its radical form.

Complete step by step solution:
The given term is \[14\], and we need to simplify it into the radical form.
So, by seeing that number, we can say that given number is a real number and we are asked to find out its radical expression (those expressions which contain square root, cubical root or fractional in their expressions) and the number is breaking into small factors then taking a square root of it.
The simplification of the given number \[14\] into its radical form is done as
We first take the square root of \[14\] that is
\[=\sqrt{14}\]
Now we split the given number into the simplest factors, they are
\[=\sqrt{7\times 2}\]
It can solve as
\[=\sqrt{7}\times \sqrt{2}\].
Here no perfect square is present in the above form, then
The radical form of 14 is \[\sqrt{14}\] or \[\sqrt{7}\times \sqrt{2}\] which shows it is a non-perfect square (whose square root is not a whole number).

Note: Students should know about the radical expression and the method to convert the numbers to the radical expression before solving this kind of question. While solving for the square root of the number, we should be given complete concentration.