SOLUTION: The question is as followed:
Without the use of a calculator explain how in the olden days they used to evaluate the following.
Square Root of Two (2) √2
Square Root
Algebra.Com
Question 205460: The question is as followed:
Without the use of a calculator explain how in the olden days they used to evaluate the following.
Square Root of Two (2) √2
Square Root of Seven (7) √7
" " " Thirteen (13) √13
" " " One Hundred and sixty nine (169) √169
I'm unsure where to ever start with this.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll show you how to find the square root of 2:
Step 1) Divide 2 by 1 to get 2. Since , this means that the square root of 2 is NOT 1.
Step 2) Average the previous result 2 with the first number 1 to get:
Step 3) Divide 2 by 1.5 to get 1.33333... Since , this means that the square root of 2 is NOT 1.5
Note: you can use long division by writing it out by hand.
Step 4) Average the quotient 1.3333... with 1.5 to get
Step 5) Divide 2 by 1.41665 to get 1.41178 (take note how the numbers are getting closer). Since , this means that the square root of 2 is NOT 1.41665 (or 1.41178). But we are getting closer
Step 6) Average 1.41665 and 1.41178 to get
Step 7) Divide 2 by 1.4142 to get 1.414227. If we round the this quotient to the nearest ten-thousandth, we get 1.4142. Since this (to four places), this means that (approximately). In other words,
So to four decimal places, the square root of 2 is roughly 1.4142
So 
Follow the same logic to find the square root of 7, 13, and 169.
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