Let's solve the expression step by step to reach the result. The given expression is:
[tex]\[ \sqrt{\frac{47,269 - \frac{(649)^2}{9}}{9}} \][/tex]
1. Calculate the square of 649:
[tex]\[ 649^2 = 649 \times 649 = 420,401 \][/tex]
2. Divide this square by 9:
[tex]\[ \frac{420,401}{9} \approx 46,800.11111111111 \][/tex]
3. Subtract this result from 47,269:
[tex]\[ 47,269 - 46,800.11111111111 = 468.8888888888905 \][/tex]
4. Divide this result by 9:
[tex]\[ \frac{468.8888888888905}{9} \approx 52.09876543209894 \][/tex]
5. Finally, take the square root of the result:
[tex]\[ \sqrt{52.09876543209894} \approx 7.217947452849663 \][/tex]
So, the detailed, step-by-step result for the given expression is:
[tex]\[ \sqrt{\frac{47,269 - \frac{(649)^2}{9}}{9}} \approx 7.217947452849663 \][/tex]
