Pregunta
Identify the most simplified version of the expression below: \[ \begin{array}{ll}\frac{\sqrt{2}}{\sqrt{18}} \\ \begin{array}{ll}\text { A) } \frac{\sqrt{3}}{3} & \text { C) } \frac{5 \sqrt{3}}{3} \\ \text { B) } \frac{1}{3} & \text { D) } \frac{3 \sqrt{2}}{3}\end{array}\end{array} \]
Ask by Potter Lindsey. in the United States
Feb 27,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The expression simplifies to \( \frac{1}{3} \), which is option B.
Solución
We start by writing the expression as a single square root:
√2/√18 = √(2/18)
Simplify the fraction under the square root:
2/18 simplifies to 1/9, so we have √(1/9).
Taking the square root of 1/9 gives:
√(1/9) = 1/3.
Thus, the expression simplifies to 1/3, which is option B.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
To simplify the expression \(\frac{\sqrt{2}}{\sqrt{18}}\), we can start by rewriting \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}. \] Now we can substitute this back into our expression: \[ \frac{\sqrt{2}}{\sqrt{18}} = \frac{\sqrt{2}}{3\sqrt{2}}. \] Next, we can simplify \(\frac{\sqrt{2}}{3\sqrt{2}}\): \[ \frac{\sqrt{2}}{3\sqrt{2}} = \frac{1}{3}. \] Thus, the most simplified version of the expression is: \[ \boxed{\frac{1}{3}}. \] This corresponds to option B.
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