Is 360 a square number?
Understand the Problem
The question is asking whether the number 360 can be expressed as the square of an integer. In other words, it seeks to determine if there exists a whole number whose square equals 360.
Answer
No, 360 cannot be expressed as the square of an integer.
Answer for screen readers
No, 360 cannot be expressed as the square of an integer.
Steps to Solve
- Identify the square root of 360
To determine if 360 is a perfect square, we need to find its square root.
Calculate the square root: $$ \sqrt{360} $$
- Approximate the square root
Using a calculator or simplifying: $$ \sqrt{360} \approx 18.97 $$
Since 18.97 is not an integer, we determine that 360 is not a perfect square.
- Check for integer squares around 360
Evaluate the squares of the integers around the approximate square root value:
For 18: $$ 18^2 = 324 $$
For 19: $$ 19^2 = 361 $$
Since 360 is not equal to either 324 or 361, we confirm that there is no integer whose square equals 360.
No, 360 cannot be expressed as the square of an integer.
More Information
The number 360 is not a perfect square, which means there isn't an integer whose square is exactly 360. The closest perfect squares are 324 ($18^2$) and 361 ($19^2$).
Tips
Common mistakes include:
- Assuming that any number can be a perfect square without checking the square root.
- Miscalculating the square of nearby integers. Always check squares of integers near the approximate square root.
