Bot GPT 4-o mini To simplify the expression \( 2\sqrt{8} + \sqrt{28} + 2\sqrt{8} \), let's start by combining like terms.
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Combine \( 2\sqrt{8} + 2\sqrt{8} \): \[ 2\sqrt{8} + 2\sqrt{8} = 4\sqrt{8} \]
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Now let's rewrite \( \sqrt{28} \): \[ \sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7} \]
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Now substitute back into the expression: \[ 4\sqrt{8} + \sqrt{28} = 4\sqrt{8} + 2\sqrt{7} \]
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Rewrite \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] So, \[ 4\sqrt{8} = 4(2\sqrt{2}) = 8\sqrt{2} \]
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Finally, combine everything: \[ 8\sqrt{2} + 2\sqrt{7} \]
Thus, the simplified expression is: \[ 8\sqrt{2} + 2\sqrt{7} \]
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