How to Simplify the Radical of 45

The video tutorial explains how to simplify radicals, focusing on the example of sqrt(45). It begins by discussing the importance of identifying square numbers and memorizing them. The tutorial then demonstrates the process of simplifying sqrt(45) by expressing it as a product of square numbers, specifically 9 and 5. The instructor also explores alternative factorizations, such as 15 and 3, and explains why they are not useful for simplification. The final simplified form is presented as 3 times the square root of 5.

What is the main goal when simplifying a radical like sqrt(45)?

• To find the exact decimal value

• To rewrite it as a product of a square number

• To express it as a fraction

• To convert it into a logarithm

Which of the following is a correct factorization of 45 that helps in simplifying sqrt(45)?

• 15 * 3

• 9 * 5

• 10 * 4.5

• 6 * 7.5

What is the simplified form of sqrt(9) * sqrt(5)?

• 3 * sqrt(5)

• 5 * sqrt(3)

• sqrt(45)

• 9 * sqrt(5)

Why is the factorization 15 * 3 not useful for simplifying sqrt(45)?

• Because 15 and 3 are greater than 10

• Because 15 and 3 are prime numbers

• Because 15 and 3 are both even numbers

• Because 15 and 3 are not square numbers

What is the final simplified form of sqrt(45) as discussed in the video?

• sqrt(45)

• sqrt(9) * sqrt(5)

• 3 * sqrt(5)

• 5 * sqrt(3)