Add, Subtract, and Multiply Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root, cube root, etc. The most common radical is the square root.

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 look for pairs of factors. Each pair can be taken out of the radical as a single factor.

Front

What is the square root of 20 simplified?

Back

The square root of 20 can be simplified to 2√5.

Front

What is the process for adding or subtracting radical expressions?

Back

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

Front

What is the result of -3√20 - √5?

Back

The result is -7√5 after simplifying -3√20 to -6√5 and combining it with -√5.

Front

How do you multiply radical expressions?

Back

To multiply radical expressions, multiply the numbers outside the radicals and the numbers inside the radicals separately, then simplify if possible.

Front

What is the product of √3 and √12?

Back

The product is √36, which simplifies to 6.

Front

What is the sum of 3√5 and √20?

Back

The sum is 5√5 after simplifying √20 to 2√5.

Front

What is the simplified form of √45?

Back

The simplified form of √45 is 3√5.

Front

What is the result of 3√5 + √20 - √45?

Back

The result is 2√5 after simplifying the expression.