Solve the following equation: (3 + 512) \div \sqrt{42} =

The equation is: $$(3 + 512) \div \sqrt{42} =$$

First, calculate the sum in the parentheses:

$$3 + 512 = 515$$

So, the equation becomes:

$$515 \div \sqrt{42} =$$

Now, we need to find the square root of 42. Since 42 is not a perfect square, we'll use an approximate value. $$\sqrt{42}$$ is between $$\sqrt{36} = 6$$ and $$\sqrt{49} = 7$$. Since 42 is closer to 49, we can estimate the square root of 42 as approximately 6.5.

So, the equation becomes:

$$515 \div 6.5 \approx$$

To divide 515 by 6.5, we can perform the division:

$$\frac{515}{6.5} = \frac{5150}{65}$$

Performing the division:

     79.23
65|5150.00
   455
   ---
    600
    585
    ---
     150
     130
     ---
      200
      195
      ---
        5

So, $$515 \div 6.5 \approx 79.23$$

Therefore, the solution is approximately 79.23.