Simplifying Radical Expressions with the Quotient Rule

What is the quotient rule for radicals?

• The square root of a difference is the difference of the square roots.

• The square root of a quotient is the quotient of the square roots.

• The square root of a sum is the sum of the square roots.

• The square root of a product is the product of the square roots.

What is the first step in simplifying the expression \(\sqrt{24x^9} / \sqrt{3x^3}\)?

• Separate the variables.

• Divide the coefficients.

• Simplify the exponents.

• Combine the radicals into one.

What is the result of \(24 / 3\) in the context of the first example?

• 6

• 8

• 12

• 9

How do you simplify \(x^9 / x^3\) using the rules of exponents?

• Divide the exponents.

• Subtract the exponents.

• Multiply the exponents.

• Add the exponents.

What is the simplified form of \(\sqrt{8x^6}\)?

• 4x^2\sqrt{2}

• 2x^2\sqrt{2}

• 4x^3\sqrt{2}

• 2x^3\sqrt{2}

In the second example, why is it easier to split the expression?

• Because 18 is a perfect square.

• Because 49 is a perfect square.

• Because x^2 is not a perfect square.

• Because 18 is not a perfect square.

What is the simplified form of \(\sqrt{49}\)?

• 5

• 7

• 6

• 8

How can 18 be expressed to simplify the radical?

• 6 * 3

• 9 * 2

• 8 * 2.25

• 12 * 1.5

What is the square root of 9?

• 2

• 5

• 4

• 3

What is the final simplified form of \(\sqrt{18x^2} / 7\)?

• 2x\sqrt{3} / 7

• 2x\sqrt{3} / 6

• 3x\sqrt{2} / 6

• 3x\sqrt{2} / 7