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(sqrt(5r^(3)))/(sqrt(2r^(2)))

$\frac{\sqrt{5 r^{3}}}{\sqrt{2 r^{2}}}$

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Multiplication with rational exponents

Full solution

Q.

\frac{\sqrt{5 r^{3}}}{\sqrt{2 r^{2}}}

Simplify Radicands: Simplify the square roots by dividing the radicands. $\newline$ We have the expression $\frac{\sqrt{5r^{3}}}{\sqrt{2r^{2}}}$ . To simplify, we can divide the radicands (the numbers inside the square roots) and reduce the exponents where possible.
Apply Quotient Rule: Apply the quotient rule for radicals. The quotient rule for radicals states that $\sqrt{a}/\sqrt{b} = \sqrt{a/b}$ , where $a$ and $b$ are non-negative numbers. Applying this rule, we get: $(\sqrt{5r^{3}})/(\sqrt{2r^{2}}) = \sqrt{(5r^{3})/(2r^{2})}.$
Simplify Inside Square Root: Simplify the expression inside the square root. $\newline$ Now we simplify the expression inside the square root by dividing the coefficients and subtracting the exponents of like bases: $\newline$ $\sqrt{\left(\frac{5r^{3}}{2r^{2}}\right)} = \sqrt{\left(\frac{5}{2}r^{3-2}\right)} = \sqrt{\left(\frac{5}{2}r^{1}\right)}$ .
Write Final Answer: Write the final simplified expression. $\newline$ The expression inside the square root is already simplified, so we can write the final answer as: $\newline$ $\sqrt{\left(\frac{5}{2}\right)r}$ or $\sqrt{\frac{5}{2}}$ * $\sqrt{r}$ .

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