If I want to compute the following

In[6]:= 3^Sqrt[2.0]

Out[6]= 4.7288

The result is given to 5 significant digits, which is quite a small number - a pocket calculator do a lot better. I'm sure the CPU's floating point processor can do a lot better than that. I tried indicating that the 2 was know more precisely than one significant digit, by indicating a number of zeros, but again a result with only 5 significant digits is returned.

In[9]:= 3^Sqrt[2.00000000000]

Out[9]= 4.7288

Obviously I can perform the this particular calculation in arbitrary precision,

In[32]:= N[3^Sqrt[2],20] 

Out[32]= 4.7288043878374149479

but that inconvenient, and slower than desirable. Is there any way to force Mathemaitca to display about 12 digits? A standard Intel CPU should be able to handle that in the vast majority of cases.. I realise that rounding errors can be significant for some calculations, so I might have less than 12 digits, but I'm sure printing to 10 or 12 digits would be a vast improvement, and they would probably all be right.

I tried

In[16]:= N[3^Sqrt[2.000000000000000000],20]

Out[16]= 4.72880438783741495

In[17]:=  Precision[%]

Out[17]= 18.2169

which seems to do the trick, but I wonder if there's a way to display machine precision numbers to a bit more than 5 significant digits. A pocket calculator does better than that.

Dave