Feb. 17. Simplifying Radicals

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

To simplify a radical, factor the number under the radical into its prime factors, and then look for pairs of factors. Each pair can be taken out of the radical as a single factor.

$$\text{√}24 = 2\text{√}6$$ .

$$3\text{√}16 = 12$$ .

$$\text{√}150 = 5\text{√}6$$ .

$$4\text{√}75 = 20\text{√}3$$ .

$$\text{√}48 = 4\text{√}3$$ .

The principle involves breaking down the number under the radical into its prime factors and simplifying by removing pairs.

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction.

$$\text{√}x^2 = x$$ , assuming x is non-negative.