Simplifying Radicals: Key Concepts and Techniques

What is the simplest form of a radical?

• No perfect squares under the root except one

• Any number under the root

• Only prime numbers under the root

• Only integers under the root

Which of the following is a perfect square?

• 33

• 18

• 36

• 22

What does prime factorization involve?

• Breaking down a number into prime factors

• Adding numbers until primes are left

• Multiplying prime numbers

• Dividing the number by prime numbers only

What is the square root of 108 simplified using perfect squares?

• 6√3

• 10√2

• 9√2

• 3√4

How can the square root of 180 be simplified using prime factorization?

• 6√5

• 9√4

• 5√6

• 10√3

What is the result of simplifying the square root of 200?

• 20

• 14√2

• 10√2

• 100

How do you remove a radical from the denominator?

• Multiply the numerator and denominator by the radical

• Add the radical to both numerator and denominator

• Subtract the radical from the numerator

• Divide the numerator by the radical

What happens when you multiply the square root of 8 by itself?

• 16

• Square root of 16

• Square root of 64

• 8

After simplifying the square root of 40 in the denominator, what is the final expression?

• √10 over 10

• 4√10 over 40

• 2√10 over 10

• 2 over 40

What is the simplified form of the square root of 8?

• 2√2

• 4

• √4

• 8