Simplifying Radicals with Variables

Front

Define a radical expression.

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

What is the square root of a variable raised to an even power?

Back

The square root of a variable raised to an even power can be simplified by taking half of the exponent. For example, @@ ext{If } x^{2n}, ext{ then } ext{ } oot{2}{x^{2n}} = x^n@@.

Front

Simplify: @@ ext{ } oot{2}{z^4}@@

Back

Front

What is the square root of a product?

Back

The square root of a product can be expressed as the product of the square roots. For example, @@ ext{ } oot{2}{ab} = oot{2}{a} imes oot{2}{b}@@.

Front

Simplify: @@ ext{ } oot{2}{196c^5d^2}@@

Back

@@14c^2d oot{2}{c}@@.

Front

What is the cube root of a number?

Back

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, @@ ext{ } oot{3}{x} ext{ is the cube root of } x@@.

Front

Simplify: @@ ext{ } oot{3}{32}@@

Back

@@2 oot{3}{4}@@.

Front

What is the square root of a variable raised to an odd power?

Back

The square root of a variable raised to an odd power can be simplified by taking half of the exponent and leaving one factor of the variable. For example, @@ ext{If } x^{2n+1}, ext{ then } ext{ } oot{2}{x^{2n+1}} = x^n oot{2}{x}@@.

Front

Simplify: @@ ext{ } oot{2}{8x^6}@@

Back

@@2x^3 oot{2}{2}@@.

Front

What is the process of simplifying radicals?

Back

The process of simplifying radicals involves factoring out perfect squares (or cubes) from under the radical sign and simplifying the expression.