Simplifying Radicals with Variables

Front

What is a radical?

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root.

Front

How do you simplify √(a^2)?

Back

√(a^2) simplifies to |a|, which is the absolute value of a.

Front

What is the process of simplifying radicals?

Back

The process involves factoring out perfect squares from under the radical sign and simplifying the expression.

Front

What does it mean to simplify √(x^2y)?

Back

It means to express it as x√y, assuming x is non-negative.

Front

How do you simplify √(12x^4)?

Back

√(12x^4) simplifies to 2x^2√3.

Front

What is the first step in simplifying a radical expression?

Back

The first step is to factor the number or expression under the radical into its prime factors.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

How do you simplify √(a^4b^2)?

Back

√(a^4b^2) simplifies to a^2b.

Front

What is the rule for simplifying √(xy)?

Back

√(xy) cannot be simplified further unless x or y is a perfect square.

Front

What is the significance of the index in a radical?

Back

The index indicates the degree of the root; for example, a square root has an index of 2.