Mixed Operations with Radicals

A radical is a symbol used to represent the root of a number, most commonly the square root. For example, $$\sqrt{9}$$ represents the square root of 9, which is 3.

You can simplify it by using the property of radicals: $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$$ .

The value of $$\sqrt{16}$$ is 4.

To add radicals, they must have the same index and radicand. For example, $$\sqrt{2} + \sqrt{2} = 2\sqrt{2}$$ .

To simplify $$\sqrt{20}$$ , factor it into its prime factors: $$\sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}$$ .

The area of a rectangle is calculated using the formula: Area = $$l \cdot w$$ .

To multiply radicals, you can multiply the numbers inside the radicals: $$\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$$ .

The value of $$\sqrt{9} + 3$$ is 3 + 3 = 6.

To simplify $$\sqrt{12}$$ , factor it: $$\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$$ .

The value of $$\sqrt{a^2}$$ is |a|, the absolute value of a.