Is 54 a perfect square?
Understand the Problem
The question is asking whether the number 54 is a perfect square, which means determining if there is an integer that, when multiplied by itself, equals 54.
Answer
54 is not a perfect square.
Answer for screen readers
54 is not a perfect square.
Steps to Solve
- Finding the square root of 54
To determine if 54 is a perfect square, we first find the square root of 54.
$$ \sqrt{54} \approx 7.348 $$
- Checking for integer square
A perfect square must have an integer square root. Since $7.348$ is not an integer, we conclude that 54 is not a perfect square.
- Verifying bounds of integers
We can further verify by checking the squares of integers around $7.348$:
- The square of 7:
$$ 7^2 = 49 $$
- The square of 8:
$$ 8^2 = 64 $$
Since $49 < 54 < 64$, we confirm that there is no integer whose square equals 54.
54 is not a perfect square.
More Information
A perfect square means that the number can be expressed as the square of an integer. For example, $1, 4, 9, 16, \ldots$ are perfect squares, while 54 is not among them.
Tips
Some common mistakes include:
- Assuming that any non-integer square root indicates a perfect square.
- Miscalculating the square of nearby integers.
