Operations of Radicals

Front

What is a radical in mathematics?

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 of factors to take out of the radical.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction.

Front

Simplify: √20 - √50

Back

√20 - √50 = 2√5 - 5√2.

Front

What are like terms in radical expressions?

Back

Like terms are terms that have the same radical part. For example, 3√2 and 5√2 are like terms.

Front

Simplify: 9√33

Back

9√33 cannot be simplified further as 33 does not have any perfect square factors.

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, e.g., √a * √b = √(a*b).

Front

Simplify: 14√x / √2

Back

14√x / √2 = 7√(2x).

Front

What is the square root of a product?

Back

The square root of a product is the product of the square roots, e.g., √(ab) = √a * √b.

Front

Simplify: 6a^5b^3√3b

Back

6a^5b^3√3b is already in its simplest form.