Question

What is the radical form?

Answer 1

Hint: Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity. We can make use of laws of exponents to convert the exponential form to radical form as ${\left( a \right)^{\dfrac{x}{n}}} = \sqrt[n]{{{a^x}}}$ where n is a positive integer.

Complete step-by-step answer:
Exponent refers to the number of times a number is multiplied by itself. It is placed as a superscript of a number. It is also known as the power of a number just like the square of any number implies multiplying a number two times. It can be expressed as \[{a^p}\]where \[a\]is the number and \[p\] is the power, and \[a\] cannot be equal to zero.
We can calculate the square of any rational number which implies that we can take out the square root of any rational number. It can be a natural or decimal number. Like this we can take out the cube and any \[{n^{th}}\]power. It concludes that we can calculate the \[{n^{th}}\]root of any number.
The \[{n^{th}}\] root can be expressed as \[\sqrt[n]{x}\]where \[x\]is any number and \[n\]is the index. This form is known as the radical form. It can be read as \[x\]radical \[n\].

Note: In the radical symbol, the horizontal line is known as vinculum, the quantity under the vinculum is called the radicand and the quantity \[n\]written to the left is known as the index. If the \[{n^{th}}\] root of any number is multiplied \[{n^{th}}\]times we get the number itself.