1. The problem is to find the square root of 789. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. Since 789 is not a perfect square, we estimate the square root by finding the nearest perfect squares. 4. $28^2 = 784$ and $29^2 = 841$, so $\sqrt{789}$ is between 28 and 29. 5. To get a better estimate, use the formula for approximation: $$\sqrt{a} \approx b + \frac{a - b^2}{2b}$$ where $a=789$ and $b=28$. 6. Calculate the numerator: $789 - 784 = 5$. 7. Calculate the denominator: $2 \times 28 = 56$. 8. So the approximation is: $$28 + \frac{5}{56} = 28 + 0.0893 = 28.0893$$ 9. Therefore, the square root of 789 is approximately $28.09$.