Dividing Radicals

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Dividing radicals is a way of simplifying rational expression into an expression without any radical in the denominator. It is done by rationalizing the denominator. Rationalizing is a process that starts with a fraction having radical in the denominator and determining a fraction without any radical in the denominator. If both dividend and divisor has radical then divide the numbers outside the radical and divide the numbers inside the radicals.
 The following example shows how to divide the radicals.

Example 1: Simplify: 12 / (3√2)

Solution: Given fraction: 12 / (3√2)

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.


Example 2: Simplify:  (15√24) / (3√2)

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

Solution: In the given, the numbers are inside the radical

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

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