Linked Questions

4
votes
6answers
25k views

How to calculate square root or cube root? [duplicate]

I was reading Richard Feynman biography when I read that one time he was able to calculate the cube root of large number in his brain by just using simple facts of everyday life. So my question is ...
2
votes
3answers
7k views

How to calculate the square root of a number? [duplicate]

By searching I found few methods but all of them involve guessing which is not what I want. I need to know how to calculate the square root using a formula or something. In other words how does the ...
3
votes
2answers
2k views

Calculate more digits of square root of 2? [duplicate]

How would I calculate the next digit of the decimal representation of square root of two? 1.4142135... Say I want to calculate the digit after 5... how would I do that? I am not allowed to use a ...
2
votes
2answers
348 views

What is the sum that the square root button on calculator does so I can do it without the calculator button [duplicate]

I am not very good when it comes to Maths but the current work I am doing means I need to get better and quick. I have been teaching myself about areas, diagonals and square roots. However I am ...
0
votes
1answer
89 views

Approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ [duplicate]

I am attempting to resolve the following problem: Find an approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ using the bisection algorithm. From what I understand, $\sqrt{5}$ has ...
27
votes
16answers
40k views

Calculating the square root of 2

Since $\sqrt{2}$ is irrational, is there a way to compute the first 20 digits of it? What I have done so far I started the first digit decimal of the $\sqrt{2}$ by calculating iteratively so that ...
32
votes
6answers
19k views

How can I find the square root using pen and paper?

Okay, I know this is very basic question. I learned 2 methods in school. But now, I forget one. Here is a simple method that I know. Find the prime divisors of the number Omit the half of numbers ...
9
votes
2answers
3k views

Numerical method for finding the square-root.

I found a picture of Evan O'Dorney's winning project that gained him first place in the Intel Science talent search. He proposed a numerical method to find the square root, that gained him $100,000 ...
2
votes
3answers
131 views

What is the smallest integer integer $m$ such that $2^m > 10^{21}$?

What is the smallest integer integer $m$ such that $2^m > 10^{21}$? I determined that since $2^{50} > 5^{20}$, we see that $2^{71} > 10^{20}$. The answer is $m = 70$, but I haven't figured ...
5
votes
1answer
125 views

How does this approximation of $\sqrt[R]{n}$ work?

Decades ago, when the slide rule was the norm, and calculators with the ability to calculate square roots were the cutting edge of technology, I was given an interesting formula. It went like this: ...
1
vote
3answers
125 views

$\sqrt {144} = 12$ How can I find it without calculator?

$$12\times 12 = 144$$ If there's a question that asks me to find square roots manually, how will I find that? I know a way that's really long and boring. I actually know about the "Tree" method. Is ...
0
votes
1answer
120 views

Obtain an aproximation to $\sqrt{5}$ using other numeric methods

From the original problem: Find an approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ using the bisection algorithm. In which I have a function in Mathematica to do the ...