Expressing Answers in Simplest Radical Form

This tutorial teaches how to simplify radical expressions by breaking down numbers into factors, ensuring one is a perfect square. It provides examples with √45 and √180, demonstrating the process of identifying perfect square factors, separating them under individual radicals, and simplifying the expression to its simplest radical form.

What is the first step in simplifying a radical expression?

• Square the number.

• Break the number into two factors, ensuring one is a perfect square.

• Identify the largest factor.

• Divide the number by 2.

What makes a number a perfect square?

• Its square root is a whole number.

• It is divisible by 2.

• It is a prime number.

• It is an odd number.

What is the simplest radical form of the square root of 45?

• The square root of 9 times 5

• 3 times the square root of 5

• 9 times the square root of 5

• 45

Why do we separate the square root of 9 from the square root of 5 when simplifying the square root of 45?

• To make the expression more complex

• Because 9 is not a perfect square

• Because 9 is a perfect square

• Because 5 is a perfect square

What is the next step after identifying a perfect square in the factors of a number under a radical?

• Subtract the factors

• Add the factors

• Write each factor under its own radical sign

• Multiply the factors

How do you express the square root of 180 in its simplest radical form?

• 6 times the square root of 5

• 9 times the square root of 20

• 3 times the square root of 60

• 18 times the square root of 10

What factor combination is used to simplify the square root of 180?

• 9 and 20

• 12 and 15

• 10 and 18

• 6 and 30

Why is it important to check if the number under the radical has more perfect squares?

• To increase the number of steps in the process

• To simplify the expression further

• To make the expression longer

• To ensure the expression is as complex as possible

What do you do with numbers outside the radical when simplifying radical expressions?

• Subtract them

• Leave them as they are

• Divide them

• Multiply them together

What is the result of simplifying the square root of 20 in the context of the square root of 180?

• 4 times the square root of 5

• 2 times the square root of 5

• 20

• The square root of 4 times 5