Simplifying Radicals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root or cube 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 from under the radical sign.

Front

What is the square root of 16?

Back

4

Front

How do you simplify √(a^2)?

Back

√(a^2) = a, where a is a non-negative number.

Front

What is the product property of square roots?

Back

The product property states that √(a * b) = √a * √b.

Front

What is the quotient property of square roots?

Back

The quotient property states that √(a / b) = √a / √b, where b ≠ 0.

Front

How do you simplify √(50)?

Back

√(50) = √(25 * 2) = 5√2.

Front

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

Back

√(x^2y) = x√y, where x is non-negative.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer.

Front

How do you identify perfect square factors of a number?

Back

List the factors of the number and check which ones are perfect squares (e.g., 1, 4, 9, 16, etc.).