Radicals: simplify, add/sub, multiply

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify a radical?

Back

To simplify a radical, factor the number under the root into its prime factors and look for pairs (for square roots) or groups (for cube roots) to simplify.

Front

What is the product of √a and √b?

Back

√a × √b = √(a × b).

Front

How do you add or subtract radicals?

Back

You can only add or subtract radicals that have the same index and radicand (the number under the root). For example, √2 + √2 = 2√2.

Front

What is the square root of 25?

Back

√25 = 5.

Front

What is the simplified form of √(50)?

Back

√(50) = √(25 × 2) = 5√2.

Front

How do you multiply two binomials that contain radicals?

Back

Use the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second binomial.

Front

What is the area of a rectangle with length √5 and width √20?

Back

Area = length × width = √5 × √20 = √(5 × 20) = √100 = 10.

Front

What is the simplified form of 4√(16)?

Back

4√(16) = 4 × 4 = 16.

Front

What is the result of (3√2 + 2√3)(√2 - √3)?

Back

= 3√2 × √2 - 3√2 × √3 + 2√3 × √2 - 2√3 × √3 = 6 - 3√6 + 2√6 - 6 = -3√6.