The number that, when multiplied by itself, equals 225 is 15.
Understanding Perfect Squares
When a number is multiplied by itself, the result is known as a perfect square. This concept is fundamental in mathematics and is often expressed as 'n squared' (n²), where 'n' is the number.
- A perfect square is always the product of an integer multiplied by itself.
- For example, 3 times 3 (3 × 3) equals 9, so 9 is a perfect square.
- Finding the number that, when multiplied by itself, equals a given value is called finding the square root.
Finding the Number for 225
To determine which number, when multiplied by itself, results in 225, we are looking for the square root of 225. Through calculation, it is found that 15 multiplied by 15 yields 225.
It's also important to consider that both a positive and a negative number, when multiplied by themselves, can result in a positive perfect square:
- Positive Root: 15 × 15 = 225
- Negative Root: (-15) × (-15) = 225
Therefore, both 15 and -15 are numbers that, when multiplied by themselves, equal 225.
Key Calculation
The following table visually summarizes the calculations:
| Operation | Result |
|---|---|
| 15 $\times$ 15 | 225 |
| -15 $\times$ -15 | 225 |
This demonstrates that 225 is a perfect square, with its square roots being 15 and -15.
