To simplify the expression \( \sqrt{28} + \sqrt{38} \), we first simplify each square root if possible.
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Simplifying \( \sqrt{28} \): \[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]
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Next, we simplify \( \sqrt{38} \): \[ \sqrt{38} = \sqrt{2 \cdot 19} \quad \text{(does not simplify further)} \]
Now we can combine the simplified square roots: \[ \sqrt{28} + \sqrt{38} = 2\sqrt{7} + \sqrt{38} \]
Thus, the expression \( \sqrt{28} + \sqrt{38} \) simplifies to: \[ 2\sqrt{7} + \sqrt{38} \]
This is the simplified form, as \( 2\sqrt{7} \) and \( \sqrt{38} \) cannot be combined further. So, the final answer is: \[ 2\sqrt{7} + \sqrt{38} \]