AA 3.1 REVIEW- SOLVING RADICAL EQUATIONS PRACTICE

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

1. Isolate the radical: @@ oot[3]{2x+3} = 3 $$. 2. Cube both sides:$$ 2x + 3 = 27 $$. 3. Solve for x:$$ x = 12@@.

The index is 'c', which indicates the root being taken.

@@ oot[3]{a^2}@@.

1. Isolate the radical: @@ oot{15n+4} = 7 $$. 2. Square both sides:$$ 15n + 4 = 49 $$. 3. Solve for n:$$ n = 3@@.

1. Cube both sides: $$3v - 2 = 2v$$ . 2. Solve for v: $$v = 2$$ .

The principal square root of a number is the non-negative root of that number.

A square root of a number x is a number y such that $$y^2 = x$$ , while a cube root is a number y such that $$y^3 = x$$ .

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.