# Numerical approximations

```
g(x)=x^2-sqrt(2)
solve(g(x)==0,x)
[x == -2^(1/4), x == 2^(1/4)]
```

What's the best/quickest way to get numerical approximations of these values of x? Thanks.

Numerical approximations

```
g(x)=x^2-sqrt(2)
solve(g(x)==0,x)
[x == -2^(1/4), x == 2^(1/4)]
```

What's the best/quickest way to get numerical approximations of these values of x? Thanks.

add a comment

0

0

In your case, since `g`

can be seen as a polynomial, you can also look at its roots in the real double field (floating-point approximations with 53 bits of precision):

```
sage: g.polynomial(RDF).roots()
[(-1.189207115002721, 1), (1.189207115002721, 1)]
```

0

Try taking the right hand side of each solution.

```
sage: A = solve(g(x)==0,x)
sage: [a.rhs().n() for a in A]
[-1.18920711500272, 1.18920711500272]
```

where `n()`

is short for `numerical_approx()`

. There are other ways of approaching this as well, such as via the `solution_dict=True`

keyword to `solve()`

.

Asked: **
2015-06-03 18:33:02 -0600
**

Seen: **181 times**

Last updated: **Jun 05 '15**

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