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Best option is to use a calculator.

Failing that, use the Newton-Raphson method which entails making a guess at the answer and then improving on it. Repeating the procedure should lead to a better estimate at each stage.

To start with, if you want to find the square root of 405, define f(x) = x2 - 405.

Then finding the square root of 405 is equivalent to solving f(x) = 0.

Let f'(x) = 2x. This is the derivative of f(x) but you do not need to know that to use the N-R method.

Start with x0 as the first guess.

Then let xn+1 = xn - f(xn)/f'(xn) for n = 0, 1, 2, …

After a few iterations, xn will be very close to the required square root.

If you start with 20, whose square is 400, the second iteration gives a result that is accurate to 8 decimal places.

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โˆ™ 2013-08-29 17:26:48
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Q: How do you turn the square root of 405 into number or a decimal?
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