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+2).

Front

How do you simplify √(a^2)?

Back

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

Front

What is the index of a radical?

Back

The index of a radical indicates the degree of the root. For example, in √x, the index is 2 (square root), and in ∛x, the index is 3 (cube root).

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 add radical expressions?

Back

You can only add radical expressions if they have the same index and radicand. For example, √2 + √2 = 2√2.

Front

What is a rationalizing denominator?

Back

Rationalizing the denominator involves eliminating a radical from the denominator of a fraction. For example, to rationalize 1/√2, multiply the numerator and denominator by √2 to get √2/2.

Front

What is the difference between a perfect square and a non-perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer (e.g., 1, 4, 9). A non-perfect square cannot be expressed this way (e.g., 2, 3, 5).

Front

How do you simplify the expression √(x^4)?

Back

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

Front

What is the radical form of 8^(1/3)?

Back

The radical form of 8^(1/3) is ∛8.