Question

please solve don't spam.​

Answer 1

Step-by-step explanation:

This square root is one you can approximate very nicely. I did it with some mental arithmetic tricks and got an approximation that is extremely accurate. The answer is very nearly . This approximation has a relative error of just over two millionths or 2 ten-thosandths of one percent.

Here’s how. We start by noticing that is very close to . So

We then use the useful approximation when to write:

Then we get

Now it is clear that is 2% larger than 100, so if follows that is approximately 2% smaller than . So after we subtract , we need to add back 2% of .

The calculator reports the answer to slightly more precision as: