Simplifying Radicals: Numbers and Variables

This video tutorial covers the process of simplifying radicals, including handling numbers and variables. It explains how to use a list of perfect squares for simplification, addresses both even and odd exponents, and demonstrates combining number and radical parts. The tutorial includes examples and practice problems, and introduces advanced techniques for handling numbers outside radicals.

What is the square root of 36?

• 12

• 3

• 18

• 6

If you have x to the 12th under a radical, what does it simplify to?

• x to the 6th

• x to the 12th

• x to the 24th

• x squared

How do you simplify the square root of 12?

• 2 root 3

• 12

• 3 root 4

• 4 root 3

What is the result of simplifying the square root of 28?

• 7 root 4

• 4 root 7

• 28

• 2 root 7

How do you handle the square root of x to the 7th?

• x to the 6th root x

• x to the 3rd root x

• x to the 4th root x

• x to the 3.5

What is the simplified form of the square root of 64?

• 8

• 32

• 16

• 64

What does x to the 12th simplify to under a radical?

• x to the 6th

• x squared

• x to the 12th

• x to the 24th

If a radical already has a number outside, how do you handle additional numbers coming out?

• Multiply them

• Ignore them

• Add them

• Subtract them

What is left inside the radical when simplifying the square root of 25 with x to the 9th?

• 5

• x

• x squared

• None of the above

How do you simplify the square root of a product of a perfect square and another number?

• Divide the square root of the perfect square by the other number

• Subtract the square root of the perfect square from the other number

• Add the square root of the perfect square to the other number

• Take the square root of the perfect square and multiply by the other number