4. Radical Operations (Simplify, Add, Subtract)

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root. For example, √4 = 2.

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs of factors. For example, √18 can be simplified to 3√2.

Front

What is the product property of radicals?

Back

The product property states that √a * √b = √(a*b). This means you can multiply the numbers under the radical.

Front

What is the quotient property of radicals?

Back

The quotient property states that √(a/b) = √a / √b, allowing you to separate the radical of a fraction.

Front

How do you add or subtract radical expressions?

Back

You can only add or subtract radical expressions that have the same index and radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable radical.

Front

What is the difference between a radical and a rational number?

Back

A radical number involves roots (like square roots), while a rational number can be expressed as a fraction of two integers.

Front

How do you evaluate a radical expression?

Back

To evaluate a radical expression, substitute the variable with a number and simplify. For example, if x = 4, then √x = √4 = 2.

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).