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Question

The exponential form of $$\sqrt{\sqrt{2}}\times \sqrt{\sqrt { 3 } } $$ 


A
62
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B
612
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C
614
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D
6
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Solution

The correct option is C $$6^{\dfrac{1}{4}}$$
The given expression is $$ \sqrt { \sqrt { 2 }  } \times \sqrt { \sqrt { 3 }  }$$
$$ =\left( \sqrt { 2 }  \right) ^{ 1/2 } \times  \left( \sqrt { 3 }  \right) ^{ 1/2 }\\ =2^{ 1/2 \times  1/2 } \times 3^{ 1/2 \times  1/2 }\\ ={ 2 }^{ 1/4 }\times  { 3 }^{ 1/4 }\\ =\left( 2\times 3 \right) ^{ 1/4 }\\ =6^{ 1/4 } $$

Mathematics

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