Simplifying Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents 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 square root of 72?

Back

√72 = 6√2.

Front

How do you simplify √140?

Back

√140 = 2√35.

Front

What is the simplified form of 4√75?

Back

4√75 = 20√3.

Front

How do you simplify √300?

Back

√300 = 10√3.

Front

What is the simplified form of 5√80?

Back

5√80 = 20√5.

Front

What is the first step in simplifying a radical?

Back

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

Front

What are perfect squares?

Back

Perfect squares are numbers 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 of a number?

Back

To identify perfect square factors, list the factors of the number and check which ones are perfect squares.