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.