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Simplify \( \sqrt{50}+2\sqrt{72} \) to \( 5\sqrt{2}+12\sqrt{2} \), which equals \( 17\sqrt{2} \).
Solución
Calculate or simplify the expression \( \sqrt{50}+2\sqrt{72} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{50}+2\sqrt{72}\)
- step1: Simplify the root:
\(5\sqrt{2}+2\sqrt{72}\)
- step2: Simplify the root:
\(5\sqrt{2}+2\times 6\sqrt{2}\)
- step3: Multiply the terms:
\(5\sqrt{2}+12\sqrt{2}\)
- step4: Collect like terms:
\(\left(5+12\right)\sqrt{2}\)
- step5: Add the numbers:
\(17\sqrt{2}\)
Revisado y aprobado por el equipo de tutoría de UpStudy
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To simplify \( \sqrt{50} + 2 \sqrt{72} \), let's start with each square root. First, \( \sqrt{50} \) can be simplified as follows: \[ \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \] Now, for \( 2\sqrt{72} \): \[ \sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2} \] So, \( 2\sqrt{72} = 2 \cdot 6\sqrt{2} = 12\sqrt{2} \). Putting it all together: \[ \sqrt{50} + 2\sqrt{72} = 5\sqrt{2} + 12\sqrt{2} = (5 + 12)\sqrt{2} = 17\sqrt{2} \] Thus, the simplified expression is \( 17\sqrt{2} \).
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