Is 99 a perfect square?
Understand the Problem
The question is asking whether the number 99 is a perfect square, meaning whether there exists an integer whose square is equal to 99.
Answer
99 is not a perfect square.
Answer for screen readers
99 is not a perfect square.
Steps to Solve
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Identify perfect squares
To determine if 99 is a perfect square, we start by identifying the perfect squares of integers around the square root of 99. The square root of 99 is approximately $9.95$, so we will check integers $9$ and $10$. -
Calculate squares of integers
Next, we calculate the squares of the integers $9$ and $10$.
- For $9$:
$$ 9^2 = 81 $$ - For $10$:
$$ 10^2 = 100 $$
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Compare with 99
Now we compare the squares we calculated with the number 99:
- $9^2 = 81$ is less than 99.
- $10^2 = 100$ is greater than 99.
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Conclusion
Since there is no integer $n$ such that $n^2 = 99$, we conclude that 99 is not a perfect square.
99 is not a perfect square.
More Information
Perfect squares are numbers that can be expressed as the square of an integer. The next perfect squares after 81 (which is $9^2$) are 100 (which is $10^2$), confirming that 99 is not among them.
Tips
- A common mistake is to assume that if a number is close to a perfect square, it is one. It's important to check the exact squares of integers surrounding the square root to reach a proper conclusion.
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