Question

What is the definition of a radical number in math?

Answer 1

Hint: The square root or radical is related to figuring out that what should be the number which when multiplied by itself is equal to the number under the square root symbol $\sqrt{}$. This symbol is known as a radical symbol. Since in our case we have given the question in which we have to define the radical, we will first get rid of the radical and remove the square root in order to solve and get a particular original number value of radicand. There are many terms which we should know in order to know about the radical number. We will know the exact meaning of the term in our solution.

Complete step-by-step solution:
The term radical or root says that it is the mathematical opposite of an exponent, in the same manner that addition is the opposite of subtraction. The smallest radical is the square root, represented with the symbol $\sqrt{}$. And the next radical is the cube root, represented by the symbol $\sqrt[3]{}$. Also the small number in front of the radical is its index number. The index number can be any whole number .
We can also understand the different terms related to radical which are important to know as follows –
Firstly, Radical - The $\sqrt{}$ symbol that is used to denote square root of nth roots $\sqrt[n]{}$.
Second, Radical Expression - A radical expression is an expression containing a square root. Example = $\sqrt{x-5}$.
Third, Radicand - A number or expression inside the radical symbol. Example = $\sqrt{4}$, 4 is radicand .
Fourth, Radical equation - An equation containing radical expressions with variables in the radicands. Example = $\sqrt{x}-\sqrt{x-5}=1$.

Note: Always remember that the result of a radical operation is positive if the number under the radical is positive.
Keep in mind , the result is negative if the number under the radical is negative and the index number is odd.
Learn that , a negative number under the radical with an even index number produces an irrational number.
Always keep in mind that we can use prime factorisation for the number inside the radical and pull out non- radical terms or perfect squares from the inside of the square root to make the solution easier .