Simplifying the Square Root of a Number by Factorization, Sqrt(45)

The video tutorial explains how to simplify radicals using two methods: prime factorization and square numbers. It highlights the importance of understanding both methods and discusses common mistakes students make, such as incorrect factorization. The tutorial encourages using the square numbers method for efficiency but advises reverting to prime factorization if needed.

What is the prime factorization of 45?

• 3 * 3 * 5

• 5 * 5 * 3

• 2 * 3 * 5

• 3 * 3 * 3

Which of the following is the largest square number that divides into 45?

• 16

• 36

• 9

• 25

What is the simplified form of sqrt(45) using the largest square number method?

• 9 sqrt 5

• 5 sqrt 3

• sqrt 45

• 3 sqrt 5

Why is it incorrect to simplify sqrt(45) using 15 * 3?

• 15 and 3 do not multiply to 45

• 15 and 3 are not square numbers

• 15 and 3 are not prime numbers

• 15 and 3 are both even numbers

What should you do if you mistakenly use non-square numbers in simplifying radicals?

• Try a different pair of numbers

• Ignore the mistake

• Use the prime factorization method

• Use a calculator