Nth Roots and Radicals

• 7³

• 7

• 7^3/4

• 7^4/3

Simplify the following:

• A

• B

• C

• D

Write the expression in radical form.

x^3/4

• ∜x³

• ∛x⁴

• x^.75

• √x²

Write in exponential form

∛x⁷

• 3x⁷

• 7x³

Find the indicated real n^th root(s) of a. n = 8 , a = 256

• 2

• -2

• ±2

• no real roots

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

Find the indicated real n^th root(s) of a. n = 5 , a = -243

• 3

• -3

• ±3

• no real roots

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