Simplifying Radicals and Expressions

The video tutorial explains how to simplify radical expressions, focusing on avoiding fractions under radicals and radicals in denominators. It provides two examples: simplifying the square root of 72/49 using prime factorization and simplifying the square root of 45x^2/9x^2 by recognizing simplification properties. The tutorial emphasizes understanding the properties of radicals and efficient simplification techniques.

What is a radical expression not considered simplified if it contains?

• A whole number

• A negative number

• A fraction under the radical

• A decimal

What property is used to simplify the square root of a fraction?

• The square root of a fraction equals the square root of the numerator divided by the square root of the denominator

• The product of roots property

• The difference of squares property

• The sum of squares property

What is the prime factorization of 72?

• 2 x 2 x 3 x 3

• 2 x 3 x 3 x 3

• 2 x 2 x 2 x 2 x 3

• 2 x 2 x 2 x 3 x 3

What is the simplified form of the square root of 72/49?

• Square root of 2 divided by 6

• 6/7

• 7/6

• 6 square root 2 divided by 7

What is the perfect square factor of 49?

• 6

• 9

• 8

• 7

In the second example, what does 45x^2/9x^2 simplify to?

• Square root of x

• Square root of 9

• Square root of 5

• Square root of 45

What is the benefit of using the property in reverse order for the second example?

• It saves time

• It introduces more variables

• It makes the expression more complex

• It requires more steps

What is the result of simplifying 9x^2 divided by 9x^2?

• 0

• x

• 1

• 9

What is the final simplified form of the second example?

• Square root of 45

• Square root of 5

• Square root of x

• Square root of 9

What is the main takeaway from the video tutorial?

• Radicals should always be left unsimplified

• Variables make simplification impossible

• Using properties can simplify expressions efficiently

• Simplifying radicals is always complex