Simplifying, Adding, and Subtracting Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol used to represent the root of a number, most commonly the square root. For example, √x represents the square root of x.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then extract any perfect squares (or higher powers) from under the radical.

Front

What is the square root of 18 simplified?

Back

The square root of 18 simplifies to 3√2.

Front

What is the process for adding radical expressions?

Back

To add radical expressions, combine like terms. This means you can only add radicals that have the same index and radicand.

Front

What is the result of √18 - √12?

Back

The result of √18 - √12 is 3√2 - 2√3.

Front

How do you subtract radical expressions?

Back

To subtract radical expressions, like terms are combined, similar to adding. Ensure the radicals have the same index and radicand.

Front

What is the simplified form of 5√80?

Back

The simplified form of 5√80 is 20√5.

Front

What is the result of adding 4√7 - 10√7 + 7√7?

Back

The result is √7.

Front

How do you simplify √150?

Back

To simplify √150, factor it into √(25 * 6), which simplifies to 5√6.

Front

What is the simplified form of 2√24?

Back

The simplified form of 2√24 is 4√6.