Simplifying Radicals and Radical Operations

A radical is a symbol that represents the root of a number, typically the square root, cube root, etc. For example, $$\sqrt{4}$$ represents the square root of 4.

To simplify a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

@@\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$$.

The product of two radicals can be simplified by multiplying the numbers under the radicals together. For example, @@\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$$.

You can only add radicals that have the same radicand (the number under the radical). For example, @@2\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}$$.

The sum is @@\sqrt{7}$$.

To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical. For example, @@2\sqrt{5} \cdot 3 = 6\sqrt{5}$$.

The area is @@16\sqrt{6}$$.

The cube root is @@2r^2s\cdot \sqrt[3]{7r^2s}$$.

The area of a rectangle is calculated by multiplying its length by its width: Area = Length × Width.