The Radical Formula in mathematics is the opposite of an exponent, which is symbolised by the sign ” √” also known as root. The number preceding the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root. This number is written as an exponent and is a whole number that cancels the radical.

The Radical Formula is as follows

n√ x=p

x1/n = p

(x1/n)n = pn

x = pn

where,

The n√ symbol is noted as the radical of the nth root.

The index is noted as ‘n’

The expression inside the radical symbol i.e x is known as the radicand.

A number’s radical and root are interchangeable terms. The root might be an nth root, a square root, or a cube root. A radical is thus any number or phrase that has a root.The Latin word Radix, which means root, is where the word “radical” originates. The radical may be used to explain several types of roots for a number, including square, cube, fourth, and so on. The index number or degree is the number that appears before the radical. How many times the number would need to be multiplied by itself to equal the radicand is helped by this number. Similar to how addition is the opposite of subtraction and division is the opponent of multiplication, this is regarded as being the opposite of an exponent.

For example: ∛2 = 2 as 2 × 2 × 2 = 8.

The sign √ that denotes a number’s root is known as radical, and it is interpreted as x radical n or the nth root of x. The horizontal line that surrounds the number is known as the vinculum, and the number underneath it is known as the radicand. The index or degree is the number n written before the radical.

Students can use the Radical Formula page to understand the radical general rules from the Extramarks. The Extramartks come up with various kinds of examples and solved questions. A radical is a phrase that contains the number’s root. Some general guidelines for radicals are as follows:

If a number is positive, both its radical and its outcome are positive.

If an integer is negative, its radical is also negative.

Only when the number under the radical is negative and any index, including integers, will it be termed illogical.

If no index is specified, the radical will be a square root.