Question
Given \( x>0 \), simplify \( \sqrt{4 x^{18}} \) completely
Ask by Bush Fuentes. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form of √(4x¹⁸) is 2x⁹.
Solution
To simplify √(4x¹⁸), start by expressing the square root as the product of two square roots:
√(4x¹⁸) = √(4) · √(x¹⁸)
Since √(4) = 2 and x is positive (x > 0), the square root of x¹⁸ is x⁹ (because (x⁹)² = x¹⁸), therefore:
√(x¹⁸) = x⁹
Multiplying these results together gives:
√(4x¹⁸) = 2x⁹
Thus, the simplified expression is 2x⁹.
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Simplify this solution Bonus Knowledge
To simplify \( \sqrt{4 x^{18}} \), we can break it down into two parts: \( \sqrt{4} \) and \( \sqrt{x^{18}} \). First, \( \sqrt{4} = 2 \). Next, for \( \sqrt{x^{18}} \), we use the property of exponents that states \( \sqrt{x^n} = x^{n/2} \). Therefore, \( \sqrt{x^{18}} = x^{18/2} = x^9 \). Putting it all together, we have: \[ \sqrt{4 x^{18}} = \sqrt{4} \cdot \sqrt{x^{18}} = 2 \cdot x^9 = 2x^9. \] So, the simplified form of \( \sqrt{4 x^{18}} \) is \( 2x^9 \).
