Is 26 a perfect square?
Understand the Problem
The question is asking whether the number 26 is a perfect square. A perfect square is an integer that is the square of another integer. In this case, we will evaluate if there exists an integer n such that n² equals 26.
Answer
No, 26 is not a perfect square.
Answer for screen readers
No, 26 is not a perfect square.
Steps to Solve
- Identify the nearest perfect squares
First, we need to identify the perfect squares around 26. The perfect squares are found by squaring integers:
- $1^2 = 1$
- $2^2 = 4$
- $3^2 = 9$
- $4^2 = 16$
- $5^2 = 25$
- $6^2 = 36$
The nearest perfect squares are $25$ (which is $5^2$) and $36$ (which is $6^2$).
- Evaluate if 26 is a perfect square
Since $25 < 26 < 36$, we can conclude that 26 is not equal to any $n^2$ for integer values of $n$.
- Determine the square root
We can also calculate the square root of 26 to check if it's an integer:
$$ \sqrt{26} \approx 5.099 $$
Since $5.099$ is not an integer, this confirms that 26 is not a perfect square.
No, 26 is not a perfect square.
More Information
A perfect square is the product of an integer multiplied by itself, such as $1, 4, 9, 16, 25$, etc. Since 26 lies between the squares of 5 and 6, it does not qualify as a perfect square.
Tips
- A common mistake is assuming that any number close to a perfect square is also a perfect square. Always verify by calculating the square root or checking against the list of perfect squares.
