Let's simplify and solve each of your expressions step by step.
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Add \(3\sqrt{21} + 7\sqrt{21}\): \[ (3 + 7)\sqrt{21} = 10\sqrt{21} \]
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Add \(\sqrt{19} + \sqrt{19}\): \[ (1 + 1)\sqrt{19} = 2\sqrt{19} \]
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Add \(\sqrt[3]{22} + 3\sqrt{22} + \sqrt{22}\): \[ \sqrt[3]{22} + (3 + 1)\sqrt{22} = \sqrt[3]{22} + 4\sqrt{22} \] (Note that \(\sqrt[3]{22}\) cannot be combined with \(4\sqrt{22}\) because they are different forms.)
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Subtract \(8\sqrt{23} - \sqrt{23}\): \[ (8 - 1)\sqrt{23} = 7\sqrt{23} \]
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Calculate the difference in miles run by Jake on Monday and Tuesday (7√6 miles and 5√6 miles): To find the difference: \[ 7\sqrt{6} - 5\sqrt{6} = (7 - 5)\sqrt{6} = 2\sqrt{6} \]
So, the answers are:
- \(10\sqrt{21}\)
- \(2\sqrt{19}\)
- \(\sqrt[3]{22} + 4\sqrt{22}\)
- \(7\sqrt{23}\)
- \(2\sqrt{6}\) miles difference.