Simplifying, Adding, Subtracting, and Multiplying 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

How do you simplify √a × √b?

Back

√a × √b = √(a × b).

Front

What is the simplified form of √(a^2)?

Back

The simplified form is |a|.

Front

What is the product of √3 and √15?

Back

√3 × √15 = √(3 × 15) = √45 = 3√5.

Front

How do you add or subtract radicals?

Back

You can only add or subtract radicals with the same index and radicand.

Front

What is the simplified form of 3√18?

Back

3√18 = 3√(9 × 2) = 3 × 3√2 = 9√2.

Front

What is the result of 3√2 - 3√18?

Back

3√2 - 3√18 = 3√2 - 9√2 = -6√2.

Front

How do you simplify √10 ⋅ √45?

Back

√10 ⋅ √45 = √(10 × 45) = √450 = 15√2.

Front

What is the simplified form of √25?

Back

√25 = 5.

Front

What is the simplified form of √(4 × 30)?

Back

√(4 × 30) = √4 × √30 = 2√30.