Simplifying Radicals with variables

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^2)?

Back

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

Front

What is the product property of radicals?

Back

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

Front

How do you simplify √(x^2y)?

Back

√(x^2y) simplifies to |x|√y.

Front

What is the quotient property of radicals?

Back

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

Front

How do you simplify √(x^4)?

Back

√(x^4) simplifies to x^2.

Front

What is the first step in simplifying a radical expression?

Back

The first step is to factor the expression under the radical into perfect squares.

Front

How do you simplify √(12x^2)?

Back

√(12x^2) simplifies to 2|x|√3.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction.

Front

How do you rationalize 1/√2?

Back

Multiply the numerator and denominator by √2 to get √2/2.