Simplifying Radicals (with Variables)

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, and 25 are perfect squares.

Front

What is a perfect cube?

Back

A perfect cube is a number that can be expressed as the cube of an integer. For example, 1, 8, 27, and 64 are perfect cubes.

Front

Which number is both a perfect square and a perfect cube?

Back

64 is both a perfect square (8^2) and a perfect cube (4^3).

Front

What is the index of a radical?

Back

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

Front

What happens when you take the square root of a negative number?

Back

The square root of a negative number is not a real number; it results in an imaginary number.

Front

What is the result of @@ oot{3}{-108x^3y^2z^3}@@?

Back

The result is @@-3xz oot{3}{4y^2}@@.

Front

What is the significance of the index being odd when dealing with negative numbers under a radical?

Back

When the index is odd, the radical can yield a negative solution, allowing for real numbers.

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root or cube root.

Front

What is the process of simplifying radicals?

Back

Simplifying radicals involves rewriting the expression in a simpler form, often by factoring out perfect squares or cubes.

Front

What is the relationship between perfect squares and their square roots?

Back

The square root of a perfect square is always an integer.