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.

Answer

The approximate value of $\sqrt{77}$ is $8.775$.
Answer for screen readers

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 $8.775$.

More Information

The square root of a number is a value that, when multiplied by itself, gives the original number. Since 77 is not a perfect square, its square root is an irrational number, which means it cannot be expressed exactly as a simple fraction, but can be approximated.

Tips

  • Mistaking 77 for a perfect square when performing manual calculations.
  • Failing to check that the root falls between two whole numbers before estimating the value.
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