Rationalizing Denominators and Perfect Squares

The video tutorial explains how to rationalize denominators in fractions involving square roots. It provides two examples, demonstrating the process of making the denominator a perfect square by multiplying both the numerator and denominator by an appropriate square root. The tutorial emphasizes the importance of simplifying the expression while maintaining equivalence. The video concludes with a summary of the rationalization process.

What is the first step in rationalizing the denominator of a fraction with a square root?

• Write the square root of the fraction as the square root of the numerator divided by the square root of the denominator.

• Multiply the numerator and denominator by the same number.

• Subtract the same number from both the numerator and denominator.

• Add the same number to both the numerator and denominator.

Why do we multiply the numerator and denominator by the square root of 3y in the first example?

• To add more complexity to the expression.

• To change the value of the expression.

• To make the denominator a perfect square.

• To make the numerator a perfect square.

What is the result of multiplying the square root of 3y by itself?

• 3y

• 9y

• 6y

• y

In the first example, what is the simplified form of the denominator after rationalization?

• 6xy

• 2y

• 9xy

• 3y

What is the first step in simplifying the square root of 18y in the second example?

• Divide 18y by 2.

• Multiply 18y by 2.

• Add 9 to 18y.

• Express 18 as a product of a perfect square and another number.

What is the simplified form of the square root of 18y?

• 2 square root 3y

• 3 square root 2y

• 6y

• 9y

In the second example, what do we multiply the numerator and denominator by to rationalize the denominator?

• Square root of 3y

• Square root of 5x

• Square root of 2y

• Square root of 18y

What is the final simplified form of the expression in the second example?

• Square root of 10xy divided by 6y

• Square root of 5x divided by 3y

• Square root of 20xy divided by 9y

• Square root of 15xy divided by 6y

What is the purpose of rationalizing the denominator?

• To change the value of the expression.

• To ensure the denominator is a rational number.

• To make the expression more complex.

• To simplify the numerator.

What is a perfect square in the context of rationalizing denominators?

• A number that can be divided by 2.

• A number that is greater than 10.

• A number that is less than 5.

• A number that can be expressed as the square of an integer.