Question
Simplify. \[ \sqrt{25 z^{14}} \] Assume that the variable \( z \) represents a positive real number.
Ask by Gibson Pena. in the United States
Mar 11,2025
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Answer
The simplified expression is \( 5z^7 \).
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To simplify \(\sqrt{25 z^{14}}\), we can break it down into its components. First, we know that \(\sqrt{25} = 5\). Next, for the variable part, we can simplify \(\sqrt{z^{14}}\). Since we assume \(z\) is a positive real number, we can apply the exponent rule: \(\sqrt{z^{14}} = z^{14/2} = z^7\). Putting this all together, we have: \[ \sqrt{25 z^{14}} = \sqrt{25} \cdot \sqrt{z^{14}} = 5 \cdot z^7 = 5z^7. \] The simplified form is thus \(5z^7\).