(1) Write Gauss'law for magnetism in the form of maxwell equation.
(2) Write the value of `(1)/(sqrt(mu_(0)epsilon_(0)))`

Explanation

### Step-by-Step Solution

**(1) Write Gauss' law for magnetism in the form of Maxwell's equation.**

Gauss' law for magnetism states that the total magnetic flux through a closed surface is zero. This can be expressed mathematically as:

\[ \oint \mathbf{B} \cdot d\mathbf{S} = 0 \]

Where:
- \(\oint\) denotes a closed surface integral,
- \(\mathbf{B}\) is the magnetic field,
- \(d\mathbf{S}\) is a differential area vector on the closed surface.

This equation indicates that there are no magnetic monopoles; magnetic field lines are always closed loops.

In the context of Maxwell's equations, Gauss' law for magnetism can also be represented in differential form as:

\[ \nabla \cdot \mathbf{B} = 0 \]

This indicates that the divergence of the magnetic field \(\mathbf{B}\) is zero, reinforcing the idea that magnetic monopoles do not exist.

**(2) Write the value of \(\frac{1}{\sqrt{\mu_0 \epsilon_0}}\)**

From electromagnetic theory, particularly from Maxwell's equations, we know that the speed of light \(c\) in a vacuum is given by the relationship:

\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

Where:
- \(\mu_0\) is the permeability of free space,
- \(\epsilon_0\) is the permittivity of free space.

Thus, we can express:

\[ \frac{1}{\sqrt{\mu_0 \epsilon_0}} = c \]

The speed of light in a vacuum is approximately:

\[ c \approx 3 \times 10^8 \text{ m/s} \]

### Final Answers
1. Gauss' law for magnetism in Maxwell's equation form: \(\nabla \cdot \mathbf{B} = 0\) or \(\oint \mathbf{B} \cdot d\mathbf{S} = 0\).
2. \(\frac{1}{\sqrt{\mu_0 \epsilon_0}} = 3 \times 10^8 \text{ m/s}\).

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