To determine whether the number 243463 is a perfect square, we need to follow these steps:
1. Understand the Concept of a Perfect Square:
A perfect square is a number that can be expressed as the product of an integer with itself. For example, 25 is a perfect square because it can be written as [tex]\(5 \times 5\)[/tex].
2. Find the Square Root:
The next step is to find the integer part of the square root of 243463. This means finding the largest integer whose square is less than or equal to 243463.
3. Evaluate the Square of the Nearest Integer:
Once we have the integer square root, say [tex]\( \text{sqrt\_number} \)[/tex], compute [tex]\( \text{sqrt\_number} \times \text{sqrt\_number} \)[/tex] and see if it matches 243463.
After evaluating, we find:
- The integer square root of 243463 is 493.
- However, [tex]\( 493 \times 493 = 243049 \)[/tex] and [tex]\( 243049 \neq 243463 \)[/tex].
Since the square of 493 does not equal 243463, 243463 is not a perfect square. The integer square root of 243463 is 493, and we can conclude that the number is not a perfect square.
