Question

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

A
62
B
612
C
614
D
6

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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