Summary: Radicals

Radical - simple meaning

Radical means the root of a number or expression. Roots can be square, cube or in general an nth root. The symbol '√' shows a root. The number written before the radical is the index (degree). The number under the radical is the radicand. A radical is the inverse (opposite) of an exponent.

Radical definition and parts

The radical symbol '√' is read as "n^th root of x" or "x radical n". The horizontal line over the radicand is the vinculum.

• Radical equation - an equation that has a radical.
• Radical expression - an expression inside a root.
• Radical inequality - an inequality that has a radical.

General rules for radicals

• If the number under a radical is positive, the result is positive.
• If the number under a radical is negative, the result is negative.
• If the number under a radical is negative and the index is even, the result will be an irrational number.
• If no index is shown, the radical means a square root.
• Numbers with the same radical and same index can be multiplied under one radical.
• Numbers with the same radical and same index can be divided under one radical.
• A radical can be split into factors under the same index.
• A radical can be written in exponent form; the inverse exponent 1/n corresponds to the nth root.

Radical formula

To remove an nth root, raise both sides to the power n.

• n√x = p
• x^1/n = p
• (x^1/n)ⁿ = pⁿ
• x = pⁿ
• The symbol n√ is the radical of the n^th root; 'n' is the index; the expression inside is the radicand.