Use the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √48x³/√3x

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Rewrite the given expression as a single fraction under one square root: \( \frac{\sqrt{48x^3}}{\sqrt{3x}} = \sqrt{\frac{48x^3}{3x}} \).

Simplify the fraction inside the square root by dividing the coefficients and subtracting the exponents of \(x\) (using the property \( \frac{a^m}{a^n} = a^{m-n} \)): \( \frac{48x^3}{3x} = 16x^{3-1} = 16x^2 \).

Substitute the simplified fraction back under the square root: \( \sqrt{16x^2} \).

Use the property of square roots \( \sqrt{a^2} = a \) (for \(a > 0\)) to simplify \( \sqrt{16x^2} \) into \( 4x \).

The simplified expression is \( 4x \).

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