Simplify, Add, and Subtract Radicals

Front

What is a radical?

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 √a × √b?

Back

√a × √b = √(a × b), meaning you can multiply the numbers under the radical.

Front

What is √(a/b)?

Back

√(a/b) = √a / √b, meaning you can separate the radical into the numerator and denominator.

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

How do you simplify √24?

Back

√24 = √(4 × 6) = √4 × √6 = 2√6.

Front

What is the simplified form of √128?

Back

√128 = √(64 × 2) = √64 × √2 = 8√2.

Front

How do you add radicals?

Back

You can only add radicals if they have the same radicand (the number under the radical). For example, √2 + √2 = 2√2.

Front

What is the simplified form of 2√27 + 3√3?

Back

2√27 + 3√3 = 2(3√3) + 3√3 = 6√3 + 3√3 = 9√3.

Front

What is the square root of 200?

Back

The square root of 200 is 10√2.