873595
I was not sure how to right this so i will also say it 87 radical 53595. I could do this with a calculator.
First simplify a bit:
Now, there are many methods you could use to obtain a numerical approximation of .
If you know calculus, you can use the Newton-Raphson method to find the zeros of the equation .
Alternatively, try the Babylonian method: For ,When choosing your initial value, 77 makes a good choice: . Good luck!
- Choose an arbitrary positive start value (try to pick one close to the root).
- Let be the average of and , i.e. .
- Repeat steps 2 and 3 until you reach the desired accuracy.
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.