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 ³√(x+2).

Front

What is the conjugate of a binomial expression?

Back

The conjugate of a binomial expression a + b√c is a - b√c. It is used to rationalize denominators.

Front

How do you simplify √(a) * √(b)?

Back

√(a) * √(b) = √(a*b). For example, √3 * √12 = √(36) = 6.

Front

What is the process to simplify radical expressions?

Back

To simplify radical expressions, factor the number under the radical into perfect squares and simplify. For example, √(18) = √(9*2) = 3√2.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction. This is often done by multiplying the numerator and denominator by the conjugate.

Front

How do you add radical expressions?

Back

To add radical expressions, combine like terms. For example, 2√3 + 3√3 = 5√3.

Front

What is the difference between like and unlike radicals?

Back

Like radicals have the same index and radicand (the number under the root), while unlike radicals do not. For example, 2√3 and 3√2 are unlike.

Front

How do you subtract radical expressions?

Back

To subtract radical expressions, combine like terms. For example, 5√2 - 2√2 = 3√2.

Front

What is the product of two conjugates?

Back

The product of two conjugates (a + b) and (a - b) is a² - b². For example, (3 + √5)(3 - √5) = 9 - 5 = 4.

Front

How do you divide radical expressions?

Back

To divide radical expressions, simplify the expression and rationalize the denominator if necessary. For example, (√12)/(√3) = √(12/3) = √4 = 2.