The square root of 3
The square root of 3 is the height of an equilateral triangle with side 2. Its value is 1.73205080756887729352744634150587236694280525381038…, irrational (an algebraic number).
How to work it out
- 1
What it is: the height of an equilateral triangle with side 2.
- 2
The first 100 digits, computed exactly with big-integer arithmetic:
- 3
1.73205080 7568877293 5274463415 0587236694 2805253810 3806280558 0697945193 3016908800 0370811461 8675724857 56
- 4
Its continued fraction is [1; 1; 2; 1; 2; 1; 2; 1; 2; 1, …]. Cutting it off gives the best fractions for a given size of denominator, such as 2/1, 5/3, 7/4.
LaTeX source of the formulas on this page
\[ \sqrt{3} = 1.732050807568\ldots \]
\[ \sqrt{3} \]How often each digit appears in the first 100 digits (computed)
| Digit | Count |
|---|---|
| 0 | 15 |
| 1 | 8 |
| 2 | 8 |
| 3 | 9 |
| 4 | 7 |
| 5 | 13 |
| 6 | 9 |
| 7 | 11 |
| 8 | 14 |
| 9 | 6 |
Best fractions from the continued fraction (computed)
| Fraction | Decimal | Error |
|---|---|---|
| 1/1 | 1.00000000000 | 7.32e-1 |
| 2/1 | 2.00000000000 | 2.68e-1 |
| 5/3 | 1.66666666667 | 6.54e-2 |
| 7/4 | 1.75000000000 | 1.79e-2 |
| 19/11 | 1.72727272727 | 4.78e-3 |
| 26/15 | 1.73333333333 | 1.28e-3 |
| 71/41 | 1.73170731707 | 3.43e-4 |
| 97/56 | 1.73214285714 | 9.20e-5 |
Questions
What is the value of The square root of 3?
1.73205080756887729352744634150587236694280525381038…
Is The square root of 3 irrational?
It is irrational (an algebraic number).
What are the first 10 digits of The square root of 3?
1.7320508075.
What is a good fraction for The square root of 3?
2/1 is simple, and 7/4 is accurate to about 1.8e-2.