5.3-Multiplying Radicals

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 product of two square roots?

Back

The product of two square roots can be simplified using the property: @@ oot{a}{x} imes oot{a}{y} = oot{a}{xy}@@.

Front

Simplify: @@ oot{2}{8} imes oot{2}{2}@@

Back

@@ oot{2}{8} imes oot{2}{2} = oot{2}{16} = 4@@.

Front

What is the square root of a product?

Back

The square root of a product can be expressed as: @@ oot{a}{xy} = oot{a}{x} imes oot{a}{y}@@.

Front

Simplify: @@ oot{3}{27}@@

Back

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

Front

What is the square root of a quotient?

Back

The square root of a quotient can be expressed as: @@ oot{a}{rac{x}{y}} = rac{ oot{a}{x}}{ oot{a}{y}}@@.

Front

Simplify: @@rac{ oot{5}{25}}{ oot{5}{5}}@@

Back

@@rac{ oot{5}{25}}{ oot{5}{5}} = rac{5}{ oot{5}{5}} = oot{5}{5} = 1@@.

Front

Define the term 'rationalizing the denominator'.

Back

Rationalizing the denominator involves eliminating any radicals from the denominator of a fraction.

Front

Simplify: @@rac{1}{ oot{3}{2}}@@

Back

@@rac{1}{ oot{3}{2}} imes rac{ oot{3}{4}}{ oot{3}{4}} = rac{ oot{3}{4}}{2}@@.

Front

What is the result of multiplying two radicals with the same index?

Back

The result is the radical of the product: @@ oot{n}{a} imes oot{n}{b} = oot{n}{ab}@@.