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) = 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

How do you simplify √(x^2y)?

Back

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

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 √(x^4)?

Back

√(x^4) = x^2, where x is non-negative.

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) = √(4 * 3 * x^2) = 2x√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 the denominator of 1/√2?

Back

Multiply the numerator and denominator by √2: 1/√2 * √2/√2 = √2/2.