Wolfram.com
WolframAlpha.com
WolframCloud.com
Wolfram Language
Example Repository
Ready-to-use examples of the Wolfram Language
Primary Navigation
Categories
Astronomy
Audio Processing
Calculus
Cellular Automata
Chemistry
Complex Systems
Computer Science
Computer Vision
Control Systems
Creative Arts
Data Science
Engineering
Finance & Economics
Finite Element Method
Food & Nutrition
Geography
Geometry
Graphs & Networks
Image Processing
Life Sciences
Machine Learning
Mathematics
Optimization
Physics
Puzzles and Recreation
Quantum Computation
Signal Processing
Social Sciences
System Modeling
Text & Language Processing
Time-Related Computation
Video Processing
Visualization & Graphics
Alphabetical List
Submit a New Resource
Learn More about
Wolfram Language
Related Pages
Related Symbols
Sqrt
Related Categories
Mathematics
Finding the Square Root of 2
Find the square root of 2 by making successive guesses
Example Notebook
Open in Cloud
Download Notebook
Guess that it might be 1.5:
I
n
[
1
]
:
=
1
.
5
^
2
O
u
t
[
1
]
=
2
.
2
5
That was too big; try something smaller:
I
n
[
2
]
:
=
1
.
2
5
^
2
O
u
t
[
2
]
=
1
.
5
6
2
5
Needs to be bigger again:
I
n
[
3
]
:
=
1
.
3
3
3
^
2
O
u
t
[
3
]
=
1
.
7
7
6
8
9
And bigger still:
I
n
[
4
]
:
=
1
.
4
4
^
2
O
u
t
[
4
]
=
2
.
0
7
3
6
Smaller:
I
n
[
5
]
:
=
1
.
4
^
2
O
u
t
[
5
]
=
1
.
9
6
Bigger:
I
n
[
6
]
:
=
1
.
4
1
^
2
O
u
t
[
6
]
=
1
.
9
8
8
1
Bigger:
I
n
[
7
]
:
=
1
.
4
2
^
2
O
u
t
[
7
]
=
2
.
0
1
6
4
Smaller:
I
n
[
8
]
:
=
1
.
4
1
5
^
2
O
u
t
[
8
]
=
2
.
0
0
2
2
3
Getting very close:
I
n
[
9
]
:
=
1
.
4
1
4
^
2
O
u
t
[
9
]
=
1
.
9
9
9
4
Even closer:
I
n
[
1
0
]
:
=
1
.
4
1
4
1
^
2
O
u
t
[
1
0
]
=
1
.
9
9
9
6
8
Agreeing to 5 digits:
I
n
[
1
1
]
:
=
1
.
4
1
4
2
^
2
O
u
t
[
1
1
]
=
1
.
9
9
9
9
6
The difference:
I
n
[
1
2
]
:
=
2
-
%
O
u
t
[
1
2
]
=
0
.
0
0
0
0
3
8
3
6
The exact result:
I
n
[
1
3
]
:
=
N
[
S
q
r
t
[
2
]
,
3
0
]
O
u
t
[
1
3
]
=
1
.
4
1
4
2
1
3
5
6
2
3
7
3
0
9
5
0
4
8
8
0
1
6
8
8
7
2
4
2
1
Related Symbols
Sqrt
Publisher Information
Contributed by:
Stephen Wolfram