Question

Can anyone solve this problem?​

Answer 1

`\sqrt{2 + \sqrt{2 + \sqrt{81 + 2 √(1568) } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{81 + 2 * 28 √(2) } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{81 + 56 √(2) } } } \\ = \sqrt{2 + \sqrt{2 + √(81 + 79.2) } } \\ = \sqrt{2 + \sqrt{2 + √(160.2) } } \\ = \sqrt{2 + \sqrt{2 + 4 √(10) } } \\ = \sqrt{2 + √(2) \sqrt{1 + √(2) √(10) } } \\ = \sqrt{2 + √(2) \sqrt{1 + √(20) } } \\ = \sqrt{2 + √(2) \sqrt{1 + 2 √(5) } } \\ = \sqrt{2 + √(2) * √(5.5) } \\ = \sqrt{2 + √(11) } \\ = √(2 + 3.3) \\ = √(5.3) = 2.3`

`thank \: you`

Answer 2

• 1 + √2

Explanation:

Start with the inner root:

• 81 + 2√1568 = 49 + 2*28√2 + 32 = 7² + 2*7*4√2 + (4√2)² = (7 + 4√2)²

Move to next one:

• 2 + 7 + 4√2 = 1 + 2*2√2 + 8 = 1² + 2*2√2 + (2√2)² = (1 + 2√2)²

The last one:

• 2 + 1 + 2√2 = 1 + 2√2 + 2 = 1² + 2*1*√2 + (√2)² = (1 + √2)²

The root of the last one is:

• 1 + √2