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The simplified form of \( -8 \sqrt{384} \) is \( -64\sqrt{6} \) or approximately \( -156.767344 \).
Solución
Calculate or simplify the expression \( -8\sqrt{384} \).
Calculate the value by following steps:
- step0: Calculate:
\(-8\sqrt{384}\)
- step1: Simplify the root:
\(-8\times 8\sqrt{6}\)
- step2: Multiply the terms:
\(-64\sqrt{6}\)
The simplified form of \( -8 \sqrt{384} \) is \( -64\sqrt{6} \) or approximately \( -156.767344 \).
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Simplifique esta solución The Deep Dive
To simplify \( -8 \sqrt{384} \), we start by breaking down \( 384 \) into its prime factors. Notice that \( 384 = 64 \times 6 \), and since \( 64 = 8^2 \), we can simplify \( \sqrt{384} \) as \( \sqrt{64 \times 6} = \sqrt{64} \times \sqrt{6} = 8 \sqrt{6} \). Therefore, \( -8 \sqrt{384} = -8 \times 8 \sqrt{6} = -64 \sqrt{6} \). Now, if you need to calculate \( -64 \sqrt{6} \) numerically, \( \sqrt{6} \) is approximately \( 2.45 \), leading to a final answer of about \( -156.8 \) in rounded decimals.
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