Multiplying Radical Expressions

Front

Define 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 product of two radical expressions?

Back

The product of two radical expressions can be simplified by multiplying the numbers outside the radicals and the numbers inside the radicals separately.

Front

Simplify: (√a)(√b)

Back

√(a*b) - The product of two square roots is the square root of the product.

Front

What is the square root of a product?

Back

The square root of a product is equal to the product of the square roots of each factor: √(a*b) = √a * √b.

Front

Simplify: (3√2)(4√3)

Back

12√6 - Multiply the coefficients (3*4) and the radicands (√2*√3) to get 12√(2*3).

Front

What is the coefficient in a radical expression?

Back

The coefficient is the number in front of the radical. For example, in 5√x, 5 is the coefficient.

Front

Simplify: (5√7)(2√14)

Back

10√98 or 70√2 - Multiply the coefficients (5*2) and simplify √(7*14).

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in its simplest form, removing any perfect square factors from under the radical.

Front

Simplify: (√8)(√2)

Back

√16 = 4 - Combine the radicals to get √(8*2) and simplify.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.