Simplifying Radicals and Expressions

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 square root?

Back

To simplify a square root, factor the number under the root into its prime factors and look for pairs of factors. Each pair can be taken out of the root as a single factor.

Front

Simplify: √32

Back

4√2

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

Simplify: √(a^2)

Back

a (for a ≥ 0) because the square root of a squared number is the number itself.

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: √(ab) = √a * √b.

Front

Simplify: √(45x^4y^7)

Back

3x^2y^3√(5y) because 45 = 9 * 5, x^4 = (x^2)^2, and y^7 = y^6 * y.

Front

What is the square root of a quotient?

Back

The square root of a quotient is equal to the quotient of the square roots: √(a/b) = √a / √b.

Front

Simplify: (5 + 4√3)(3 + √3)

Back

27 + 17√3 using the distributive property (FOIL method).

Front

What does it mean to rationalize the denominator?

Back

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