To simplify the expression \( 5 - \sqrt{2 + \frac{3}{5} - \sqrt{}} \), we first need to clarify if there was a typo or misunderstanding in the expression, as it does not appear to be correctly formed.
Assuming you meant \( 5 - \sqrt{2 + \frac{3}{5}} \), we can work towards simplifying it:
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Start with the expression inside the square root: \[ 2 + \frac{3}{5} = \frac{10}{5} + \frac{3}{5} = \frac{13}{5} \]
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Now plug this into the square root: \[ \sqrt{2 + \frac{3}{5}} = \sqrt{\frac{13}{5}} = \frac{\sqrt{13}}{\sqrt{5}} = \frac{\sqrt{13} \cdot \sqrt{5}}{5} = \frac{\sqrt{65}}{5} \]
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Next, substitute this back into the original expression: \[ 5 - \frac{\sqrt{65}}{5} \]
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To combine, write 5 as a fraction with the same denominator: \[ 5 = \frac{25}{5} \] Hence, \[ 5 - \frac{\sqrt{65}}{5} = \frac{25 - \sqrt{65}}{5} \]
This is the simplified version given the assumption. However, if your original expression was intended to be different, please provide clarification for accurate simplification or assistance.
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