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$\frac{9\sqrt{6}}{\sqrt{3}}$

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Cube roots of positive perfect cubes

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Q.

\frac{9\sqrt{6}}{\sqrt{3}}

Simplify Expression: Let's first simplify the expression $9\sqrt{6} / \sqrt{3}$ . We can rewrite the square roots in the expression as fractional exponents. $\sqrt{6}$ can be written as $6^{(1/2)}$ and $\sqrt{3}$ can be written as $3^{(1/2)}$ . So, the expression becomes $9 \times 6^{(1/2)} / 3^{(1/2)}$ .
Rewrite Square Roots: Now, we can simplify the expression by dividing the coefficients and the exponents separately. $\newline$ First, divide the coefficients: $9 / 1 = 9$ . $\newline$ Then, use the property of exponents to divide the terms with the same base: $6^{(1/2)} / 3^{(1/2)} = (6/3)^{(1/2)}$ .
Divide Coefficients and Exponents: Simplify the fraction inside the exponent: $(\frac{6}{3}) = 2$ . So, the expression now is $9 \times 2^{\frac{1}{2}}$ .
Simplify Exponents: $2^{\frac{1}{2}}$ is the square root of $2$ , so we can rewrite the expression as $9\sqrt{2}$ .
Final Simplified Form: Therefore, the final simplified form of the expression $9\sqrt{6}$ divided by $\sqrt{3}$ is $9\sqrt{2}$ .

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