Radical Operations

A radical is a symbol used to indicate the root of a number, most commonly the square root. For example, $$\text{√}x$$ represents the square root of x.

The square root of 16 is 4, since $$4^2 = 16$$ .

$$\text{√}12 = \text{√}(4 \times 3) = \text{√}4 \times \text{√}3 = 2\text{√}3$$ .

The result is $$7\text{√}2$$ after simplifying.

You can combine like radicals by adding or subtracting their coefficients. For example, $$3\text{√}2 + 2\text{√}2 = (3 + 2)\text{√}2 = 5\text{√}2$$ .

The simplified form is $$9\text{√}2$$ .

To simplify a radical expression means to rewrite it in a simpler form, often by factoring out perfect squares or cubes.

The value is 0, since the terms cancel each other out.

The simplified form is $$-3\text{√}10$$ .

A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.