Simplifying Higher Radicals w/ Variables

Front

Define a higher radical.

Back

Front

What is the cube root of a number?

Back

Front

How do you simplify @@ oot[3]{128u^4v^6}@@?

Back

@@ oot[3]{128u^4v^6} = 4uv^2 oot[3]{2u}@@.

Front

What is the fourth root of a number?

Back

Front

How do you simplify @@ oot[4]{80b}@@?

Back

@@ oot[4]{80b} = 2 oot[4]{5b}@@.

Front

What is the significance of variables in higher radicals?

Back

Variables in higher radicals can represent unknown quantities and can be simplified similarly to constants, following the same rules of exponents.

Front

How do you simplify @@ oot[3]{-189n^8}@@?

Back

@@ oot[3]{-189n^8} = -3n^2 oot[3]{7n^2}@@.

Front

What is the fifth root of a number?

Back

Front

How do you simplify @@-4 oot[5]{192x^2y^5z}@@?

Back

@@-4 oot[5]{192x^2y^5z} = -8y oot[5]{6x^2z}@@.

Front

What is the process of simplifying higher radicals?

Back

To simplify higher radicals, factor the expression under the radical into perfect powers and extract those powers outside the radical.