To solve the expression \( \sqrt{2} + 7\sqrt{2} \), you can combine the terms since they are like terms (both containing \( \sqrt{2} \)).
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\( \sqrt{2} + 7\sqrt{2} = (1 + 7)\sqrt{2} \)
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Combine the coefficients: \[ (1 + 7) = 8 \]
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So, you have: \[ 8\sqrt{2} \]
Therefore, the answer is \( 8\sqrt{2} \).