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The following example shows how to divide the radicals.

This fraction has radical in the divisor.

Rationalize the denominator, dividing by √2 on both sides

12 / (3√2) = (12 * √2)/ (3√2) * √2

= (12/3) * (√2 / √2√2) = 4 * √2 / 2 = 2√5

Therefore 12 / (3√2) = 2√5.

**Solution:** In the given fraction both numerator and denominator has radicals.

So, divide the numbers outside the radical and divide the numbers inside the radicals separately.

(15√24) / (3√2) = (15 / 3) (√24 / √2) = 5√12.

This √12 can be written as √4 * √3 = 2√3

Therefore, (15√24) / (3√2) = 5 * 2√3 = 10√3.

**Example 3: Simplify: √24 / √18**

Divide the numbers inside the radicals by 2

√24 / √18 = (√24/2) / (√18/2) = √12 / √9

We know √9 = 3 and

√12 = √ 4. 3 = 2 √3

Hence, √12 / √9 = 2 √3 / 3

Therefore, √24 / √18 = (2√3) / 3