Question
Simplify. \( \sqrt{x^{13}} \) Assume that the variable represents a positive real
Ask by Malone Ryan. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt{x^{13}} = x^{6}\sqrt{x} \)
Solution
Calculate or simplify the expression \( \sqrt(x^{13}) \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt{x^{13}}\)
- step1: Rewrite the exponent:
\(\sqrt{x^{12+1}}\)
- step2: Expand the expression:
\(\sqrt{x^{12}\times x}\)
- step3: Use the properties of radicals:
\(\sqrt{x^{12}}\times \sqrt{x}\)
- step4: Simplify the root:
\(x^{6}\sqrt{x}\)
The simplified form of \( \sqrt{x^{13}} \) is \( x^{6}\sqrt{x} \).
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Simplify this solution Extra Insights
To simplify \( \sqrt{x^{13}} \), we can use the property of square roots that states \( \sqrt{a^b} = a^{b/2} \). Applying this here gives us: \[ \sqrt{x^{13}} = x^{13/2} \] Since \( 13/2 \) can be expressed as \( 6.5 \), we have: \[ x^{13/2} = x^{6.5} = x^6 \cdot x^{0.5} = x^6 \sqrt{x} \] Thus, the simplified form is: \[ x^6 \sqrt{x} \] So, \( \sqrt{x^{13}} = x^6 \sqrt{x} \) is the final answer.
