Pregunta
QUESTION 6 6.1. Determine between which two consecutive intogers the following su lies: \( \sqrt{17} \) \( \qquad \) \( \qquad \) 6.2. Calculate the following without the use of a calculator: 6.2.1. \( \sqrt{16 x^{4} y^{6}}= \) \( \qquad \) 6.2.2. \( \sqrt{0,25}-\sqrt[3]{\frac{1}{8}} \) \( \qquad \) \( \qquad \) \( \qquad \)
Ask by Smith Mills. in South Africa
Mar 04,2025
Solución de inteligencia artificial de Upstudy
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6.1. √17 is between 4 and 5.
6.2.1. √(16x⁴y⁶) = 4x²y³.
6.2.2. √0.25 - ∛(1/8) = 0.
Solución
6.1. We know that √16 = 4 and √25 = 5, so √17 is between 4 and 5.
6.2.1. To simplify √(16x⁴y⁶), break it into parts:
√(16) = 4,
√(x⁴) = x² (assuming x is nonnegative),
√(y⁶) = y³ (assuming y is nonnegative).
Thus, √(16x⁴y⁶) = 4x²y³.
6.2.2. Calculate √0.25 - ∛(1/8):
√0.25 = 0.5 (since 0.5² = 0.25),
∛(1/8) = 0.5 (since 0.5³ = 0.125 = 1/8).
So, 0.5 - 0.5 = 0.
Final Answers:
• 6.1: √17 lies between 4 and 5.
• 6.2.1: √(16x⁴y⁶) = 4x²y³.
• 6.2.2: √0.25 - ∛(1/8) = 0.
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Bonus Knowledge
To find between which two consecutive integers \(\sqrt{17}\) lies, we can observe that \(\sqrt{16} = 4\) and \(\sqrt{25} = 5\). Since \(17\) is between \(16\) and \(25\), we know that \(\sqrt{17}\) is between \(4\) and \(5\). Therefore, the answer is 4 and 5. For \(6.2.1\), we can simplify \(\sqrt{16 x^{4} y^{6}} = \sqrt{16} \cdot \sqrt{x^{4}} \cdot \sqrt{y^{6}} = 4 \cdot x^{2} \cdot y^{3} = 4x^{2}y^{3}\). For \(6.2.2\), we calculate \(\sqrt{0.25} = 0.5\) and \(\sqrt[3]{\frac{1}{8}} = \frac{1}{2}\). Thus, \( \sqrt{0.25} - \sqrt[3]{\frac{1}{8}} = 0.5 - 0.5 = 0\).
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