2 Answers

110.1135777277621 around about

Without a calculator:

You can get an idea by finding two consecutive numbers that 21,125 is in between. The two consecutive numbers are 145 and 146. Then square them.

145^2 =  21,025

146^2 =  21,316

So, 21,125 is in between 21,025 and 21,316.

Now you know that the square root of 21,125 is going to start with 145. ?

Now comes the guessing part:

145.5^2 = 21,170.25   >   too high

145.1^2 = 21,054.01   >   too low

So, the square root of 21,125 is between 145.1 and 145.5.

145.4^2 = 21,141.16   >   too high

145.3^2 = 21,112.09   >   this will work

145.35^2 = 21,126.6225   >   too high

145.34^2 = 21,123.7156   >   this will work

145.345^2 = 21,125.169025   >   a little too much

145.344^2 = 21,124.878336   >   this will work

It takes a lot of time without a calculator. But at least you'll get an idea for finding the square root of numbers that are not a whole number.

Calculator:

145.34441853748633026659628846753 > with an answer like this, use a calculator!