Combine the following expressions. \( 2 \sqrt{5}+5 \sqrt{5} \) \( 7 \sqrt{5} \) 35 \( 7 \sqrt{10} \)
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To combine these expressions, we'll start by adding together the like terms. The first two expressions, \(2 \sqrt{5}\) and \(5 \sqrt{5}\), have the same radical part. When combined, they yield: \(2 \sqrt{5} + 5 \sqrt{5} = (2 + 5) \sqrt{5} = 7 \sqrt{5}\). Now, we have \(7 \sqrt{5}\) from the above and the second expression \(7 \sqrt{5}\) already given, so: \(7 \sqrt{5} + 7 \sqrt{5} = 14 \sqrt{5}\). Finally, putting this all together, we have 14√5 and the constants 35 and \(7 \sqrt{10}\) which can't be simplified with \(14 \sqrt{5}\). Therefore, the final combined expression is: \(14 \sqrt{5} + 35 + 7 \sqrt{10}\).
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