Simplifying Square Roots with Prime Factorization

The video tutorial explains how to simplify square roots when the radicand is not a perfect square. It introduces the concept of perfect square factors and demonstrates the simplification process using the square root of 72 as an example. The tutorial also covers the prime factorization method as an alternative approach, illustrated with the square root of 1,575. The video concludes with a summary of the methods discussed.

What is the term used for the number under the square root symbol?

• Radical

• Coefficient

• Radicand

• Exponent

Which of the following is a perfect square factor of 72?

• 8

• 12

• 36

• 18

What is the simplified form of the square root of 72?

• 5 square root 3

• 8 square root 3

• 6 square root 2

• 9 square root 2

What is the first step in using prime factorization to simplify a square root?

• Multiply by 10

• Identify the perfect square factors

• Write out the prime factorization

• Divide the number by 2

How many factors of 2 are there in the prime factorization of 72?

• 1

• 2

• 3

• 4

What is the simplified form of the square root of 1,575?

• 15 square root 7

• 25 square root 7

• 10 square root 5

• 20 square root 3

Which number is a prime factor of 1,575?

• 6

• 9

• 8

• 5

What is the result of simplifying the square root of 3 x 3?

• 1

• 9

• 6

• 3

Which of the following is NOT a step in simplifying square roots using prime factorization?

• Leave non-paired factors under the square root

• Identify pairs of equal factors

• Multiply all prime factors

• Simplify each pair to a single factor

What is the benefit of using prime factorization to simplify square roots?

• It only works for even numbers

• It is faster than other methods

• It requires no calculations

• It helps identify all perfect square factors