Let's solve each of these equations step by step.

### 1. \(\sqrt{x^2} = 8\)

The square root of \(x^2\) is the absolute value of \(x\):
\[ |x| = 8 \]

This gives us two possible solutions:
\[ x = 8 \quad \text{or} \quad x = -8 \]

### 2. \(\sqrt{9x^2} = 10\)

First, simplify the expression inside the square root:
\[ \sqrt{9x^2} = \sqrt{9} \cdot \sqrt{x^2} = 3|x| \]

Set this equal to 10:
\[ 3|x| = 10 \]

Divide both sides by 3:
\[ |x| = \frac{10}{3} \]

This gives us two possible solutions:
\[ x = \frac{10}{3} \quad \text{or} \quad x = -\frac{10}{3} \]

### 3. \(\sqrt{4x^2 - 19} = 0\)

Since the square root of a number is zero only when the number itself is zero:
\[ 4x^2 - 19 = 0 \]

Solve for \(x\):
\[ 4x^2 = 19 \]
\[ x^2 = \frac{19}{4} \]
\[ x = \pm \sqrt{\frac{19}{4}} \]
\[ x = \pm \frac{\sqrt{19}}{2} \]

### 4. \(\sqrt{49x^2} = |-14|\)

First, simplify the absolute value:
\[ |-14| = 14 \]

Now, simplify the expression inside the square root:
\[ \sqrt{49x^2} = \sqrt{49} \cdot \sqrt{x^2} = 7|x| \]

Set this equal to 14:
\[ 7|x| = 14 \]

Divide both sides by 7:
\[ |x| = 2 \]

This gives us two possible solutions:
\[ x = 2 \quad \text{or} \quad x = -2 \]

### Summary of Solutions:
1. \( x = 8 \) or \( x = -8 \)
2. \( x = \frac{10}{3} \) or \( x = -\frac{10}{3} \)
3. \( x = \frac{\sqrt{19}}{2} \) or \( x = -\frac{\sqrt{19}}{2} \)
4. \( x = 2 \) or \( x = -2 \)