If \(x = \sqrt{225} + \sqrt{484}\), what is the value of \(x^2 - \left[(\sqrt{225})^2 + (32)^2\right]\)?
120
First, evaluate the square roots: \(\sqrt{225} = 15\) and \(\sqrt{484} = 22\).
So \(x = 15 + 22 = 37\).
Calculate \(x^2 = 37^2 = 1369\).
Calculate the bracket: \((\sqrt{225})^2 + (32)^2 = 225 + 1024 = 1249\).
Therefore, \(x^2 - \left[(\sqrt{225})^2 + (32)^2\right] = 1369 - 1249 = 120\).
Hence, the value of the expression is 120.
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