A method for approximating can be traced back to the Babylonians. The formula is given by the recursively defined sequence where k is an initial guess as to the value of the square root. Use this...

A method for approximating can be traced back to the Babylonians. The formula is given by the recursively defined sequence

where k is an initial guess as to the value of the square root. Use this recursive formula to approximate the following square roots by finding a₅. Compare this result to the value provided by your calculator.