Final answer:
7 is the largest integer smaller than the square root of 50 because 7 squared is 49, which is the largest perfect square less than 50. The square root of 50 is slightly more than 7, thus 7 is the highest whole number that squares to less than 50.
Step-by-step explanation:
The question is asking to explain why 7 is the largest integer smaller than the square root of 50. To answer this, we need to consider what the square root of 50 is. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, is close to but less than 50.
Calculating the square of each integer, we see:
- 6 × 6 = 36
- 7 × 7 = 49
- 8 × 8 = 64
On comparing these values, 49 is the largest perfect square that is less than 50. Therefore, 7 is the largest integer whose square is less than 50. Any larger integer would exceed 50 when squared.
Mathematically, if we take the square root of 50, we get a number that is slightly more than 7, but since we are looking for the largest whole number smaller than this value, 7 is the answer. This is an example of applying the knowledge of square numbers and the properties of the square root to find the correct integer.