Adding and Subtracting 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

How do you simplify a radical expression?

Back

To simplify a radical expression, factor out perfect squares (or cubes) from under the radical sign and simplify. For example, √(4x) = 2√x.

Front

What does it mean to add radical expressions?

Back

To add radical expressions, combine like terms. This means you can only add radicals that have the same index and radicand. For example, √2 + √2 = 2√2.

Front

What does it mean to subtract radical expressions?

Back

To subtract radical expressions, like terms are combined similarly to addition. For example, 3√5 - 2√5 = 1√5 or √5.

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 ³√x, the index is 3 (cube root).

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, 16 are perfect squares.

Front

How do you evaluate a radical expression?

Back

To evaluate a radical expression, substitute the variable with a number and simplify. For example, to evaluate √(x) when x=9, √(9) = 3.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction. For example, √2 is irrational.

Front

What is the conjugate of a radical expression?

Back

The conjugate of a radical expression is formed by changing the sign between two terms. For example, the conjugate of (a + √b) is (a - √b).

Front

How do you rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator. This eliminates the radical from the denominator.