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[tex]18\sqrt{2} = \sqrt{3} \cdot r^{3}[/tex]
we aim to solve for ( r ).
Step 1: Simplify the Exponent
Simplify the exponent in the original equation.
[tex]18\sqrt{2} = \sqrt{3} \cdot r^3[/tex]
Step 2: Isolate ( r³)
Divide both sides of the equation by ( \sqrt{3}) to isolate ( r³):
[tex]r^3 = \frac{18\sqrt{2}}{\sqrt{3}}[/tex]
Step 3: Simplify the Fraction
Simplify the right-hand side of the equation. To do this, we need to simplify the fraction:
[tex]\frac{18\sqrt{2}}{\sqrt{3}}[/tex]
To simplify this, multiply the numerator and denominator by ( \sqrt{3} ):
[tex]\frac{18\sqrt{2}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{18\sqrt{2} \cdot \sqrt{3}}{3}[/tex]
[tex]\frac{18\sqrt{6}}{3}[/tex]
[tex]6\sqrt{6}[/tex]
[tex]r^3 = 6\sqrt{6}[/tex]
[tex]r = \sqrt[3]{6\sqrt{6}}[/tex]