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 surdfactor is called the rationalizing factor of the given surd.
1. Divide: √x by √y
Solution:
√x by √y
= √x ÷ √y
= √x/√y
= \(\sqrt{\frac{x}{y}}\)
2. Divide the first surd by the second surd: √32, √8
Solution:
√32 divided by √8
= √32 ÷ √8
= \(\sqrt{\frac{32}{8}}\)
= √4
= 2.
3. Find the quotient dividing the surd √96 by the surd √16.
Solution:
Required quotient
= √96 ÷ √16
= \(\sqrt{\frac{96}{16}}\)
= √6.
4. Divide: √5 by √7
Solution:
√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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