Multiplying and Dividing Radicals

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

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 (for square roots) or triplets (for cube roots) to simplify.

Front

What is the product of two radicals?

Back

The product of two radicals can be simplified by multiplying the numbers under the radicals together, then simplifying the resulting radical.

Front

What is the quotient of two radicals?

Back

The quotient of two radicals can be simplified by dividing the numbers under the radicals, then simplifying the resulting radical.

Front

How do you multiply a radical by a whole number?

Back

To multiply a radical by a whole number, simply multiply the whole number by the coefficient of the radical.

Front

What is the cube root of 125?

Back

The cube root of 125 is 5, since 5 x 5 x 5 = 125.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4 x 4 = 16.

Front

How do you simplify √(a^2b)?

Back

√(a^2b) = a√b, where a is a positive number.

Front

What is the simplified form of √(x^4)?

Back

The simplified form of √(x^4) is x^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.