Algebra 2 Radical Operations 6.1-6.5

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, $$\text{sqrt}(x)$$ is a radical expression.

Multiply the numerator and denominator by $$\text{sqrt}(x)$$ to rationalize the denominator: $$\frac{\text{sqrt}(x)}{x}$$ .

The conjugate is $$a - b\text{sqrt}(c)$$ .

To add radical expressions, they must have the same index and radicand. For example, $$\text{sqrt}(2) + \text{sqrt}(2) = 2\text{sqrt}(2)$$ .

Cube both sides to eliminate the radical: $$2x - 5 = 27$$ , then solve for x: $$x = 16$$ .

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

The square root of a negative number is an imaginary number, represented as $$i$$ , where $$i = \text{sqrt}(-1)$$ .

To find the difference, subtract g(x) from f(x): $$f(x) - g(x)$$ .

This function represents a vertical shift up by 3 units.

The value is |x|, the absolute value of x.