Radicals with Nth Root

An expression containing a radical with index n is in simplest form when these three conditions are met.

• No radicands have perfect nth powers as factors.

• No radicands contain negative numbers.

• No radicands contain fractions.

• No radicals appear in the numerator of a fraction.

• No radicals appear in the denominator of a fraction.

Write in simplest form. ∛500

• 167 ⅔

• 5 ∛4

• 10 √5

• 3 ∛167

To rationalize a denominator of 2 - √7

• multiply the numerator and denominator by √7

• multiply the denominator by 2 + √7

• multiply the numerator and denominator by 2 - √7

• multiply the numerator and denominator by 2 + √7

• multiply the denominator by √7

Simplify ∛(27d¹²)

• 9d⁴

• 3d⁴

• 3d⁹

• 9d⁹

An expression that contains a square root.

• Rationalize the Denominator

• Equation

• Power

• Radical

One of the steps that may be necessary to simplify the radical expression is what?

• inverse function

• radical equation

• composition of function

• rationalizing the denominator

The number under the radical symbol is called what?

• radical

• square root

• radicand

• index

y=√3x - 5 is what type of function?

• inverse

• extraneous

• square root

• radical

The positive number square root.

• nth root

• principal root

• radical function

• index

Equations with radicals that have variables in the radicand are called what?

• radical equations

• composition of function

• radical expressions

• radical inequalities