How do you convert square root of 32 into a decimal without using a calculator?
First of all, we can simplify the problem observing that
Now, recall that taking the square root of a number means to consider that number to the power of a half, and so
The problem is written in a simple form, since
Without using a calculator, the only thing you can do is trying to approximate from above and below, as it follows:
Now you can try to square some decimal (and this can be done by hand), and you will find that
You can keep going and find the second decimal digit, and so on, but of course the calculation will get tougher with each steps without a calculator