The uploader probably showed two methods to show that there is more than one method to solve the problem. However, I think that only a few people solved the problem using the 1st method. The 2nd method should be recommended because the calculations of 1st method are complicated, it takes more time, and there is a risk of making mistakes. For such an easy problem, it is important to solve it quickly, not just to get the answer right.
The uploader probably showed two methods to show that there is more than one method to solve the problem. However, I think that only a few people solved the problem using the 1st method. The 2nd method should be recommended because the calculations of 1st method are complicated, it takes more time, and there is a risk of making mistakes. For such an easy problem, it is important to solve it quickly, not just to get the answer right.
Japanese Math Olympiad: √(3 + √8) + √(3 - √8) =?
3 = √9 > √8, √(3 + √8) + √(3 - √8) > 0
3 ± √8 = 3 ± 2√2 = (√2)² ± 2√2 + 1 = (√2 ± 1)²
√(3 + √8) + √(3 - √8) = √[(√2 + 1)²] + √[(√2 - 1)²] = (√2 + 1) + (√2 - 1) = 2√2
Very clearly and well explained.
Thank you !
This is typical problem of 8th Math class.
Anyway, good solution - I like 2nd method! ;)
Thanks a lot !
Можно возвести в квадрат, а потом извлечь
Ответ 2 корня из двух. Можно сразу использовать тождество (a+b) в квадрате.
2 корня из 2