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