87http://upload.wikimedia.org/math/9/0...e95ece8fdc.png3595I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.

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- Jul 2nd 2008, 10:45 AMMistaMistaHelp with square root without calculator
87

__http://upload.wikimedia.org/math/9/0...e95ece8fdc.png3595__I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.

- Jul 2nd 2008, 11:35 AMReckoner
First simplify a bit: $\displaystyle 87\sqrt{53595} = 87\sqrt{9\cdot5955} = 261\sqrt{5955}$

Now, there are many methods you could use to obtain a numerical approximation of $\displaystyle \sqrt{5955}$.

If you know calculus, you can use the Newton-Raphson method to find the zeros of the equation $\displaystyle x^2 - 5955 = 0$.

Alternatively, try the Babylonian method: For $\displaystyle \sqrt{S}$,- Choose an arbitrary positive start value $\displaystyle x_0$ (try to pick one close to the root).
- Let $\displaystyle x_{n+1}$ be the average of $\displaystyle x_n$ and $\displaystyle \frac S{x_n}$, i.e. $\displaystyle x_{n+1} = \frac12\left(x_n + \frac S{x_n}\right)$.
- Repeat steps 2 and 3 until you reach the desired accuracy.

- Jul 2nd 2008, 11:50 AMmasters

The best manual method I have found is discussed here: How to Find Square Roots Without a Calculator - by E. Oosterwal

It is much like long division. Follow the example given. Then try your radical. It's really quite simple. No guess work involved.