If \(x = \sqrt{5776}\) and \(y = \sqrt{2025}\), find \(\dfrac{x^{2} - y^{2}}{x - y}\).
121
Use the identity \(\dfrac{x^{2} - y^{2}}{x - y} = \dfrac{(x + y)(x - y)}{x - y} = x + y\) (valid since \(x \neq y\)).
Evaluate \(x = \sqrt{5776} = 76\) (because \(76^{2} = 5776\)) and \(y = \sqrt{2025} = 45\) (because \(45^{2} = 2025\)).
Therefore \(x + y = 76 + 45 = 121\).
Hence, the value of the given expression is 121.
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