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Sqrt

Mathematics

Finding the Square Root of 2

Find the square root of 2 by making successive guesses

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Guess that it might be 1.5:

In[1]:=

1.5^2

Out[1]=

2.25

That was too big; try something smaller:

In[2]:=

1.25^2

Out[2]=

1.5625

Needs to be bigger again:

In[3]:=

1.333^2

Out[3]=

1.77689

And bigger still:

In[4]:=

1.44^2

Out[4]=

2.0736

Smaller:

In[5]:=

1.4^2

Out[5]=

1.96

Bigger:

In[6]:=

1.41^2

Out[6]=

1.9881

Bigger:

In[7]:=

1.42^2

Out[7]=

2.0164

Smaller:

In[8]:=

1.415^2

Out[8]=

2.00223

Getting very close:

In[9]:=

1.414^2

Out[9]=

1.9994

Even closer:

In[10]:=

1.4141^2

Out[10]=

1.99968

Agreeing to 5 digits:

In[11]:=

1.4142^2

Out[11]=

1.99996

The difference:

In[12]:=

2-%

Out[12]=

0.00003836

The exact result:

In[13]:=

N[Sqrt[2],30]

Out[13]=

1.41421356237309504880168872421

Related Symbols

Sqrt

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Contributed by: Stephen Wolfram

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