Final answer:
To solve for √196²+315², each number is squared, their squares are added together, and finally the square root of this sum is taken. The resulting value is 371.
Step-by-step explanation:
To calculate the expression √196²+315², we need to square each number and then add the results together before taking the square root of the sum:
- Square 196 to get 196² = 38416.
- Square 315 to get 315² = 99225.
- Add the squares: 38416 + 99225 = 137641.
- Take the square root of the sum: √137641.
The square root of 137641 is 371, which is the result of the expression.
Pythagorean theorem and square root are key concepts used in this solution, which involves calculating the magnitude of the resultant of two perpendicular vectors represented by their lengths.