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 number?

Back

Front

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

Back

Front

What is the process of simplifying radicals?

Back

The process of simplifying radicals involves rewriting the radical expression in a simpler form, often by factoring out perfect squares or cubes.

Front

Simplify: @@ ext{ } oot{2}{45x^4y^7}@@

Back

@@3x^2y^3 oot{2}{5y}@@.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, etc.

Front

Simplify: @@ ext{ } oot{2}{144k^3}@@

Back

@@12k oot{2}{k}@@.

Front

What does it mean to factor out a perfect square in a radical?

Back

Factoring out a perfect square means to identify and extract the largest square factor from under the radical to simplify the expression.

Front

Simplify: @@ ext{ } oot{2}{68p^3}@@

Back

@@2p oot{2}{17p}@@.

Front

What is the general form of simplifying a radical with variables?

Back

The general form is to separate the coefficients and variables, simplifying each part individually, and then combining them.