Mathematics

Nine Standard >> Operation on surds | Part-3

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How to convert surds of any order to another order


1. Convert \(\sqrt[3]{5}\) into a surd of order 6

Solution:
 \(\sqrt[3]{5}=5^{\frac{1}{3}}=5^{\frac{1 \(\times 2}{3 \times 2}}\)
   \(=5^{\frac{2}{6}}=(5^{2})^{\frac{1}{6}}\)
   \(=\sqrt[6]{25}\)

2. Convert \(\sqrt{2}\) into a surd of order 12

Solution:
 \(\sqrt{2}=\sqrt[2 \times 6]{2^{6}}=\sqrt[12]{64}\)

How to convert surds of different order into a surd of same order.

3. \(\sqrt[3]{4}, \sqrt[4]{3}\)
    Find which is greater within the above numbers?

Solution:

   \(\sqrt[3]{4}, \sqrt[4]{3}\)
   LCM of 3 and 4 is 12
  \(\sqrt[3]{4}=\sqrt[3 \times 4]{4^{4}}
        =\sqrt[12]{256}\)
        
  \(\sqrt[4]{3}=\sqrt[4 \times 3]{3^{3}}
        =\sqrt[12]{27}\)

  So, \(\sqrt[3]{4}\) is greater

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