What is the square root 3 times square root 6?

Hint: Here in this question we have been asked to find the value of square root 3 times square root 6. Firstly we will write the given verbal expression in mathematical form in order to simplify it. Then we have to simplify the number inside the square root to its reduced form and then multiply the reduced numbers to get the final square root value.

Complete step-by-step solution:
Now considering from the question we have been asked to find the value of square root 3 times square root 6.
The mathematical form of the given verbal expression “square root 3 times square root 6” will be given as $\Rightarrow \sqrt{3\times \sqrt{6}}$ . As we have been asked for the square root 3 times square root 6 we have multiplied the numbers of square root 3 and square root 6.
Now we will further simplify this expression and write it as $\Rightarrow \sqrt{3\times \sqrt{6}}=\sqrt{3\times \sqrt{3\times 2}}$ since 6 is the product of 2 and 3.
Now we will simplify and write it as $\Rightarrow \sqrt{{{3}^{\dfrac{3}{2}}}\times {{2}^{\dfrac{1}{2}}}}$ .
By further simplifying this we will have $\Rightarrow {{\left( {{3}^{\dfrac{3}{2}}}\times {{2}^{\dfrac{1}{2}}} \right)}^{\dfrac{1}{2}}}$ .
Hence we can conclude that the value of square root 3 times square root 6 will be given as $\left( {{3}^{\dfrac{3}{4}}}\times {{2}^{\dfrac{1}{4}}} \right)$.

Note: During the process of answering questions of this type we should be very careful while converting the given verbal expression into mathematical form. Only when the mathematical form of the given verbal expression is correct we will end up having the right conclusion. For example someone can consider it as $\sqrt{3\times 6}$ then they will end up having $3\sqrt{2}$ as an answer.