Find the value of ‘x’ that satisfies the equation : \(\sqrt{136 + \sqrt{57 + \sqrt{49}}} + \sqrt{x} = 19\)
49
Nested square roots are simplified from the innermost root outwards, replacing each perfect square by its root before moving to the next layer.
Step 1 — \(\sqrt{49} = 7\), so \(\sqrt{57 + 7} = \sqrt{64} = 8\).
Step 2 — \(\sqrt{136 + 8} = \sqrt{144} = 12\).
Step 3 — \(12 + \sqrt{x} = 19 \Rightarrow \sqrt{x} = 7 \Rightarrow x = 49\). The value 7 is the square root of x, not x itself; 14 and 343 do not satisfy the equation.
49 option is correct.
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