Pregunta
Simplify. Assume \( m \) is greater than or equal to zero. \( \sqrt{28 m^{2}} \)
Ask by Welch Blake. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The simplified form is \( 2\sqrt{7} \times m \).
Solución
Calculate or simplify the expression \( \sqrt{28m^2} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{28m^{2}}\)
- step1: Write as a product:
\(\sqrt{4\times 7m^{2}}\)
- step2: Write in exponential form:
\(\sqrt{2^{2}\times 7m^{2}}\)
- step3: Reorder the terms:
\(\sqrt{2^{2}m^{2}\times 7}\)
- step4: Use the properties of radicals:
\(\sqrt{2^{2}m^{2}}\times \sqrt{7}\)
- step5: Simplify the root:
\(2\sqrt{7}\times m\)
The simplified form of \( \sqrt{28m^{2}} \) is \( 2\sqrt{7} \times m \).
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Simplifique esta solución Bonus Knowledge
To simplify \( \sqrt{28 m^{2}} \), we can first factor the expression under the square root. We notice that \( 28 = 4 \times 7 \), so we can rewrite it as: \[ \sqrt{28 m^{2}} = \sqrt{4 \times 7 \times m^{2}}. \] Next, we can take the square root of each factor separately: \[ \sqrt{4} = 2, \quad \sqrt{m^{2}} = m. \] Putting it all together, we have: \[ \sqrt{28 m^{2}} = \sqrt{4} \cdot \sqrt{7} \cdot \sqrt{m^{2}} = 2m\sqrt{7}. \] Thus, the simplified form is: \[ \boxed{2m\sqrt{7}}. \]
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