Exploring Operations with Radicals

This video tutorial covers the reduction of radicals, including square roots and higher order roots, and operations such as multiplication, addition, and subtraction of radicals. It explains the concept of indices and how to handle variables within radicals. The tutorial also demonstrates how to simplify radicals and combine operations using distribution.

What is the reduced form of the square root of 75?

• 25

• 5√3

• 3√5

• 15

What is the index of a square root if no index is specified?

• 3

• 4

• 2

• 1

What is the cube root of -1?

• -1

• 1

• 0

• Undefined

How many groups of six are there in 20 X's when reducing the sixth root?

• 3

• 5

• 2

• 4

What is the simplified form of the sixth root of 256?

• 16

• 8

• 4

• 2

When multiplying two radicals with the same index, what should you do?

• Add the radicands and keep the same index

• Add the indices

• Multiply the indices

• Multiply the radicands and keep the same index

What is the simplified form of the cube root of 750?

• 6∛5

• 5√6

• 6√5

• 5∛6

What must be true for two radicals to be added together?

• They must have the same index and radicand

• They must have the same index

• They must have the same radicand

• They must be perfect squares

What is the simplified form of 3√5x - 2√5x?

• 5√x

• √5x

• 5x

• √x

What is the result of simplifying 2√3 + 4√3?

• 6√3

• 8√3

• 2√6

• 4√6