Let x = √(56+√(56 +√(56+ √(56+√(56+)…∞ )))) x = √(56+x) Squaring both the sides, x² = 56 + x x² - x – 56 = 0 x² - 8x + 7x – 56 = 0 x(x-8) + 7(x + 7) = 0 x = 8 , -7 Alternate method: Split 56 in the product of two consecutive numbers i,e. 7 & 8 and the highest number is the answer. So answer is 8.
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