Simplifying Radicals (with Variables)

Front

What is a radical?

Back

A radical is a symbol that represents the root of a number, typically the square root. For example, √4 represents the square root of 4.

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 a variable?

Back

The square root of a variable, such as √x, is expressed as x^(1/2) or √x, assuming x is a perfect square.

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 √(12x^2)?

Back

√(12x^2) simplifies to 2x√3.

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.

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 √(50)?

Back

√(50) simplifies to 5√2.