FLASHCARD: Solving Equations w/ Radicals & Rational Exponents

Front

What is a radical equation?

Back

An equation that involves a variable within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, then square both sides to eliminate the radical, and solve for the variable.

Front

What is a rational exponent?

Back

An exponent that can be expressed as a fraction, where the numerator is a power and the denominator is a root.

Front

How do you convert a rational exponent to radical form?

Back

If you have x^(m/n), it can be rewritten as the n-th root of x raised to the m power: √[n]{x^m}.

Front

What is the first step in solving the equation 2x + 5 = 15?

Back

Subtract 5 from both sides to isolate the term with the variable.

Front

What does it mean to check your answers in radical equations?

Back

Substituting the found solutions back into the original equation to verify they satisfy the equation.

Front

What is the purpose of squaring both sides of an equation?

Back

To eliminate a square root, allowing for easier solving of the equation.

Front

What is the solution to the equation √(x + 3) = 5?

Back

x = 22 (after squaring both sides and solving for x).

Front

What is the importance of checking for extraneous solutions?

Back

Some solutions may not satisfy the original equation, especially after squaring both sides.

Front

How do you rewrite the expression 27^(1/3) in radical form?

Back

It can be rewritten as the cube root of 27, which equals 3.