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 property of square roots?

Back

The product property states that @@ ext{ } oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.

Front

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

Back

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

Front

What is the sum property of square roots?

Back

The sum property states that @@ ext{ } oot{n}{a} + oot{n}{b} eq oot{n}{a + b}@@.

Front

Simplify: @@ ext{ } oot{3}{27} imes oot{3}{9}@@.

Back

@@ ext{ } oot{3}{27 imes 9} = oot{3}{243} = 9@@.

Front

What is the difference of squares formula?

Back

Front

Simplify: @@ ext{ }(2 + oot{2})^2@@.

Back

@@ ext{ }= 4 + 4 oot{2} + 2 = 6 + 4 oot{2}@@.

Front

What is the square of a binomial?

Back

Front

Simplify: @@ ext{ } oot{5}{25} imes oot{5}{5}@@.

Back

@@ ext{ } oot{5}{25 imes 5} = oot{5}{125} = 5@@.

Front

What is the rule for multiplying radicals?

Back

When multiplying radicals, multiply the numbers inside the radicals and then simplify: @@ ext{ } oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.