Division of Surds

In division of surds we need to divide a given surd by another surd the quotient is first expressed as a fraction. Then by rationalizing the denominator the required quotient is obtained with a rational denominator. For this the numerator and the denominator are multiplied by appropriate rationalizing factor. In rationalization of surds the multiplying surd-factor is called the rationalizing factor of the given surd.

1. Divide: √x by √y


√x by √y

= √x ÷ √y

= √x/√y

= \(\sqrt{\frac{x}{y}}\)

2. Divide the first surd by the second surd: √32, √8


√32 divided by √8

= √32 ÷ √8

= \(\sqrt{\frac{32}{8}}\)

= √4

= 2.

3. Find the quotient dividing the surd √96 by the surd √16.


Required quotient

= √96 ÷ √16

= \(\sqrt{\frac{96}{16}}\)

= √6.

4. Divide: √5 by √7


√5 divided by √7

= √5 ÷ √7

= \(\sqrt{\frac{5}{7}}\)

= \(\frac{\sqrt{5}\times \sqrt{7}}{\sqrt{7}\times \sqrt{7}}\), [Rationalization of denominator of surds]

= √35/7.

11 and 12 Grade Math

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