Simplifying Radical Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛(x+1).

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in a simpler form, often by removing any perfect squares (or higher powers) from under the radical sign.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4 x 4 = 16.

Front

How do you simplify √(a^2)?

Back

√(a^2) simplifies to |a|, which is the absolute value of a.

Front

What is the product property of square roots?

Back

The product property states that √(a * b) = √a * √b for any non-negative numbers a and b.

Front

How do you simplify √(50)?

Back

√(50) can be simplified to 5√2, since 50 = 25 * 2 and √25 = 5.

Front

What is the quotient property of square roots?

Back

The quotient property states that √(a/b) = √a / √b for any non-negative numbers a and b.

Front

How do you simplify √(x^4)?

Back

√(x^4) simplifies to x^2, since (x^2)² = x^4.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.

Front

How do you simplify the expression 3√(12)?

Back

3√(12) simplifies to 6√3, since √(12) = 2√3.