FLASHCARD: Solving Equations w/ Radicals & Rational Exponents

Front

To undo a square root in an equation, you need to:

Back

Square both sides.

Front

Solve for r: r^2 = 1

Back

r = 1 or r = -1.

Front

Rewrite in radical form: x^(1/2)

Back

√x.

Front

Why should you check your answer to a radical equation?

Back

To make sure the answer is not extraneous.

Front

What are the transformations of the function f(x) = -2(x - 5)^2 compared to the parent function?

Back

Reflected over the x-axis, vertical stretch, and shifted right 5.

Front

What is the definition of a radical?

Back

A radical is an expression that includes a root, such as a square root or cube root.

Front

How do you simplify √(a^2)?

Back

The simplified form is |a|.

Front

What is the relationship between rational exponents and radicals?

Back

A rational exponent indicates a root; for example, x^(1/n) is the same as √[n]{x}.

Front

Solve for x: √(x + 3) = 5

Back

x = 22.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that does not satisfy the original equation.