Simplifying Fractions with Radicals Quiz

What is the purpose of using the conjugate when simplifying fractions with radicals in the denominator?

• To add more radicals to the expression

• To eliminate the radical from the denominator

• To change the sign of the numerator

• To eliminate the radical from the numerator

In the first example, what operation is used to simplify the expression in the denominator?

• Multiplication of squares

• Sum of cubes

• Addition of squares

• Difference of squares

How is the expression 3x - 3 * radical 7 / x^2 - 7 further simplified in the first example?

• By dividing by a constant

• By factoring out a common term

• By adding a radical

• By multiplying by another conjugate

In the second example, what is the result of applying the conjugate to the denominator with two radicals?

• A sum of radicals

• A difference of squares

• A product of radicals

• A single radical

What is the simplified form of the denominator in the second example?

• 5 minus 2

• Radical 5 plus 2

• Radical 10 plus 2

• Radical 5 minus 2

In the third example, why is it necessary to multiply by 2 to the 4th power?

• To achieve a fifth root

• To simplify the numerator

• To eliminate the radical

• To create a perfect square

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

• 3 times the fifth root of 32 x^3 y^2 all over 2y

• 3 times the fifth root of 16 x^2 y^3 all over 2y

• 3 times the fifth root of 16 x^3 y^2 all over 2y

• 3 times the square root of 16 x^3 y^2 all over 2y

What is the main challenge students face in the third example?

• Not knowing how to take the fifth root

• Confusing the numerator and denominator

• Misapplying the difference of squares

• Forgetting to multiply by the conjugate

What is the purpose of multiplying by x^3 in the third example?

• To achieve a fifth root

• To create a perfect square

• To simplify the numerator

• To eliminate the radical

What is the final step in simplifying the expression in the third example?

• Dividing out the x

• Subtracting a constant

• Multiplying by the conjugate

• Adding a radical