Respuesta :

Answer:

[tex] \sqrt{2 + \sqrt{2 + \sqrt{81 + 2 \sqrt{1568} } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{81 + 2 \times 28 \sqrt{2} } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{81 + 56 \sqrt{2} } } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{81 + 79.2} } } \\ = \sqrt{2 + \sqrt{2 + \sqrt{160.2} } } \\ = \sqrt{2 + \sqrt{2 + 4 \sqrt{10} } } \\ = \sqrt{2 + \sqrt{2} \sqrt{1 + \sqrt{2} \sqrt{10} } } \\ = \sqrt{2 + \sqrt{2} \sqrt{1 + \sqrt{20} } } \\ = \sqrt{2 + \sqrt{2} \sqrt{1 + 2 \sqrt{5} } } \\ = \sqrt{2 + \sqrt{2} \times \sqrt{5.5} } \\ = \sqrt{2 + \sqrt{11} } \\ = \sqrt{2 + 3.3} \\ = \sqrt{5.3} = 2.3[/tex]

[tex]thank \: you[/tex]

Answer:

  • 1 + √2

Step-by-step 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
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