To find the number whose square is 0.2560, we need to determine the number which, when multiplied by itself, equals 0.2560. This problem can be solved by finding the square root of 0.2560.
Here’s a detailed explanation:
1. Identify the given value:
- We are given the value 0.2560.
2. Recall the definition of a square root:
- The square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y \times y = x \)[/tex]. In other words, [tex]\( y = \sqrt{x} \)[/tex].
3. Apply the square root operation:
- In this case, we need to find the square root of 0.2560, or [tex]\( \sqrt{0.2560} \)[/tex].
4. Calculate the square root:
- The number whose square is 0.2560 is [tex]\( \sqrt{0.2560} \approx 0.5059644256269407 \)[/tex].
5. Verify the result (optional step for thoroughness):
- To ensure the correctness, you could multiply the derived value by itself:
[tex]\( 0.5059644256269407 \times 0.5059644256269407 \approx 0.256 \)[/tex].
Therefore, the number whose square is 0.2560 is approximately 0.5059644256269407.
