Simplifying and Rationalizing Radical Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ oot{2}{x}@@ is a radical expression.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors and look for pairs. For example, @@ oot{2}{36} = oot{2}{6^2} = 6@@.

Front

What is the process of rationalizing a denominator?

Back

Rationalizing a denominator involves eliminating any radicals in the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.

Front

Simplify the expression: @@rac{1}{ oot{2}{x}}@@

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: @@ oot{2}{ab} = oot{2}{a} imes oot{2}{b}@@.

Front

Simplify the expression: @@ oot{2}{50}@@

Back

@@ oot{2}{50} = oot{2}{25 imes 2} = oot{2}{25} imes oot{2}{2} = 5 oot{2}@@.

Front

What does it mean to rationalize a radical expression?

Back

To rationalize a radical expression means to eliminate the radical from the denominator or to simplify the expression so that no radicals remain.

Front

Simplify the expression: @@ oot{2}{x^4}@@

Back

@@ oot{2}{x^4} = x^2@@.

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, @@ oot{3}{27} = 3@@.

Front

Simplify the expression: @@ oot{2}{8}@@

Back

@@ oot{2}{8} = oot{2}{4 imes 2} = oot{2}{4} imes oot{2}{2} = 2 oot{2}@@.