SOLUTION: Can someone assist me with this problem on my homework. Suppose that x is not a perfect square and {{{ a^2 }}} is the nearest perfect square to x. For a rough estimate of the v

Algebra ->  Square-cubic-other-roots -> SOLUTION: Can someone assist me with this problem on my homework. Suppose that x is not a perfect square and {{{ a^2 }}} is the nearest perfect square to x. For a rough estimate of the v      Log On


   

Question 1078374: Can someone assist me with this problem on my homework.
Suppose that x is not a perfect square and +a%5E2+ is the nearest perfect square to x. For a rough
estimate of the value of +sqrt%28+x+%29+, find the value of+y%5B1%5D=%0D%0A1%2F2+%28a%2Bx%2Fa%29+. This estimate can be improved by
calculating a second estimate using the first estimate +y%5B1%5D+ in place of a: +y%5B2%5D=+1%2F2++%28y%5B1%5D%2B+x%2Fy%5B1%5D%29+
Repeating this process several times will give more and more accurate estimates of x .
1. a. Which perfect square is closest to 80?
b. Use Heron’s method for approximating square roots to calculate the first estimate of the
square root of 80. Give an exact decimal answer.
c. Use the first estimate of the square root of 80 to find a more refined second estimate.
Round this second estimate to 6 decimal places.
d. Use a calculator to find the actual value of the square root of 80. List all digits shown on
your calculator’s display.
e. Compare the actual value from part (d) to the values of the first and second estimates.
What do you notice?
f. How many iterations of this process are necessary to get an estimate that differs no more
than one digit from the actual value recorded in part (d)?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So 9%5E2=81, a=9,
x=80 and you're looking for sqrt%2880%29
.
.
So then,


There's a start.
Work through the rest of the problem.