# What is the square root of 77?

#### Understand the Problem

The question is asking for the value of the square root of 77, which is a mathematical concept. We will calculate it to find the answer.

The approximate value of $\sqrt{77}$ is $8.775$.

The value of $\sqrt{77}$ is approximately $8.775$.

#### Steps to Solve

1. Identify the operation We need to find the square root of 77, which is denoted as $\sqrt{77}$.

2. Check for perfect squares Before calculating, check if 77 is a perfect square. The perfect squares close to 77 are $64$ ($8^2$) and $81$ ($9^2$). Since 77 is not a perfect square, we'll proceed to approximate.

3. Approximate the square root Because 77 lies between 64 and 81, we know that:

$$8 < \sqrt{77} < 9$$

Next, we can use a calculator or method of approximation to get a more precise value.

1. Calculate using a calculator Using a scientific calculator, find $\sqrt{77}$. The value is approximately:

$$\sqrt{77} \approx 8.775$$

The value of $\sqrt{77}$ is approximately $8.775$.