Roots and Indices Simplification

The video tutorial explains how to simplify radicals by focusing on the index and finding equal factors. It covers the simplification of square roots, cube roots, fourth roots, and fifth roots using examples like 81, 27, 16, and 243. The process involves identifying perfect square, cube, or higher power factors through prime factorization, allowing the radical to be simplified to a single factor outside the root.

What is the index of a square root if it is not explicitly given?

• 2

• 1

• 3

• 4

How can the square root of 81 be simplified?

• By finding five equal factors

• By finding two equal factors

• By finding three equal factors

• By finding four equal factors

What is the simplified form of the square root of 81?

• 7

• 10

• 8

• 9

What is the index for the cube root of a number?

• 5

• 4

• 2

• 3

How can the cube root of 27 be simplified?

• By finding four equal factors

• By finding three equal factors

• By finding two equal factors

• By finding five equal factors

What is the simplified form of the cube root of 27?

• 2

• 3

• 4

• 5

What is the index for the fourth root of a number?

• 2

• 3

• 4

• 5

How can the fourth root of 16 be simplified?

• By finding five equal factors

• By finding two equal factors

• By finding four equal factors

• By finding three equal factors

What is the simplified form of the fourth root of 16?

• 3

• 2

• 4

• 1

What is the simplified form of the fifth root of 243?

• 5

• 2

• 3

• 4