FLASHCARD: Solving Equations w/ Radicals & Rational Exponents

Front

What is a radical equation?

Back

An equation that contains 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 and then square both sides to eliminate the radical.

Front

What is an extraneous solution?

Back

A solution that does not satisfy the original equation after checking.

Front

What is the first step in solving the equation √(x + 3) = 5?

Back

Square both sides to eliminate the square root.

Front

What does it mean to check your answer in a radical equation?

Back

Substituting the solution back into the original equation to verify it holds true.

Front

What is a rational exponent?

Back

An exponent that is a fraction, representing both a root and a power.

Front

How do you convert a radical expression to a rational exponent?

Back

Use the formula: √(a) = a^(1/2) or a^(m/n) = n√(a^m).

Front

What is the relationship between square roots and squaring?

Back

Squaring a number undoes the square root, and vice versa.

Front

What is the solution to the equation x^2 = 16?

Back

x = 4 or x = -4.

Front

How do you solve an equation with a rational exponent, such as x^(2/3) = 8?

Back

Raise both sides to the reciprocal of the exponent, which is 3/2.