So there was this CS major math minor I new in college who could extract square roots of any number in his haed. Well , as long as the number wasn't too big. People always just assumed well, some people are just gifted in math. That is true but extracting square roots in your head is really easy. As long as you can add subract multiply and divide, so pretty much fourth or fifth grade math, you can extract square roots in your head.
Here is how you do it.
Lets try to extract the square root of 79.
Make a guess.
You guess a close square you know.
Here your best guess would be 9. ( you should know 9 squared is 81, a number close to ours.)
Remember the number 9.
Our number, 79, minus 81 equals -2
Twice our guess equals 18
9 plus negative two eightteenths is the square root of 79.
OK to clean up the answer.
9 equals 162 over 18. So now you can subtract 2/18ths. So that is 160/18.
two goes easily into both. ( maybe something else does also but keep it simple, you aredoing this in your head.)
That is 80/9ths
Nine times 8 is 72. So now we have 8 and 8/9ths.
This is the answer I would give. Converting into decimal takes time and reduces accuracy.
But as a comparison 8 and 8/9th s equals 8.888888888888 ect.
By calculator the square root of 79 is 8.8881944173.
Pretty close huh.
A little advise. The larger the number the more accurate the result so for numbers under ten mulitply the number by 100 and divide the result by ten.