Dividing Radicals

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Dividing radicals implies the use of the Product and Quotient Rules.

According to the Product Rule, the product of two or more numbers raised to a power equals the product of each number raised to the same power.

Dividing Radicals Formula 1

The Quotient Rule states that the radical of a quotient is equal to the quotient of the radicals of the numerator and denominator.

Dividing Radicals Formula 2

When dividing radicals (using the same index), divide under the radical first, then in front of the radical.

Example 1:

Dividing Radicals Example

Answer: $4\sqrt{2}$

Example 2:

Divide $\frac{18\sqrt{24}}{6\sqrt{3}}$.


Divide out front and divide under the radicals:

$\frac{18\sqrt{24}}{6\sqrt{3}} = 3\sqrt{8}$

Then simplify the result and solve.

$3\sqrt{8} = 3\sqrt{4 \cdot 2} = 2\sqrt{2} \cdot 3 = 6\sqrt{2}$

Answer: $6\sqrt{2}$