simplifying radicals

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

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect square factors.

Front

What is the simplest radical form of √75?

Back

5√3

Front

How do you simplify √45?

Back

√45 = √(9*5) = √9 * √5 = 3√5.

Front

What is the simplest radical form of √32?

Back

4√2

Front

How do you simplify √60?

Back

√60 = √(4*15) = √4 * √15 = 2√15.

Front

What is the simplest radical form of √125?

Back

5√5

Front

What is the first step in simplifying a radical?

Back

Factor the number 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, such as 1, 4, 9, 16, etc.

Front

How do you identify perfect square factors in a radical?

Back

Look for pairs of prime factors; each pair can be taken out of the radical as a single factor.