Simplifying Non-Perfect Square Roots

This video tutorial by Mr. J covers the process of simplifying square roots through four examples: √20, √32, √45, and √75. Each example demonstrates how to identify factors that are perfect squares and use them to simplify the square root. The video also highlights that there can be multiple methods to reach the same simplified result and emphasizes the importance of arranging the final answer with the number before the square root symbol. The tutorial concludes with a suggestion to memorize the first 12 perfect squares to aid in simplification.

What is the first step in simplifying the square root of 20?

• Find the factors of 20 that are perfect squares.

• Subtract 4 from 20.

• Divide 20 by 2.

• Multiply 20 by 4.

Which of the following is the simplified form of the square root of 20?

• 4√5

• 2√5

• 5√2

• 3√5

What are the factors of 32 that include a perfect square?

• 16 and 2

• 8 and 4

• 9 and 3

• 25 and 7

What is the simplified form of the square root of 32?

• 4√2

• 3√2

• 8√2

• 2√8

Which of the following is an alternative factorization of 32 that includes a perfect square?

• 4 and 8

• 9 and 3

• 5 and 6

• 7 and 4

What are the factors of 45 that include a perfect square?

• 6 and 3

• 7 and 5

• 8 and 6

• 9 and 5

What is the simplified form of the square root of 45?

• 2√5

• 4√5

• 3√5

• 5√3

What are the factors of 75 that include a perfect square?

• 25 and 3

• 16 and 5

• 4 and 19

• 9 and 8

What is the simplified form of the square root of 75?

• 2√15

• 4√5

• 5√3

• 3√25

What is a common practice when writing the simplified form of a square root?

• Always write the square root symbol in parentheses.

• Always put the square root symbol before the number.

• Always put the number before the square root symbol.

• Always write the number and square root symbol separately.