Question
Simplify. \( 7 \sqrt{75} \) \begin{tabular}{|l|c|c}\hline \\ \hline & \( \sqrt{ } \) & \( \square \) \\ \hline\end{tabular}
Ask by Valdez Griffin. in the United States
Feb 19,2025
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Tutor-Verified Answer
Answer
\(7\sqrt{75}\) simplifies to \(35\sqrt{3}\).
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The Deep Dive
To simplify \( 7 \sqrt{75} \), start by breaking down \( \sqrt{75} \). Since \( 75 = 25 \times 3 \), you can rewrite it as \( \sqrt{75} = \sqrt{25} \times \sqrt{3} \). Now, \( \sqrt{25} = 5 \), so \( \sqrt{75} = 5\sqrt{3} \). Therefore, \( 7 \sqrt{75} = 7 \times 5\sqrt{3} = 35\sqrt{3} \). So, the simplified form is \( 35\sqrt{3} \). Fill in the blanks: \begin{tabular}{|l|c|c}\hline \\ \hline & \( \sqrt{3} \) & \( 35 \) \\ \hline\end{tabular}