Radical Operations - Et All - 27?s

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, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

Can you combine radicals with different indices?

Back

No, you cannot combine radicals with different indices. For example, @@ oot{2}{x} + oot{3}{x}@@ cannot be simplified together.

Front

What is the simplified form of @@rac{ oot{9xy}}{ oot{2x}}@@?

Back

The simplified form is @@rac{3 oot{2y}}{2}@@.

Front

What property is used to multiply radical expressions?

Back

The distributive property is used to multiply radical expressions, not the associative property.

Front

What is the result of @@ oot{9x^5yz^3} imes oot{2xyz}@@?

Back

The result is @@3x^3yz^2 oot{2}@@.

Front

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to rewrite it in its simplest form, removing any perfect squares or cubes from under the radical.

Front

What is a perfect square?

Back

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

Front

How do you simplify @@ oot{a^2b}@@?

Back

The simplified form is @@a oot{b}@@.

Front

What is the index of a radical?

Back

The index of a radical indicates the degree of the root. For example, in @@ oot{3}{x}@@, the index is 3.

Front

What is the product rule for radicals?

Back

The product rule states that @@ oot{a} imes oot{b} = oot{a imes b}@@.