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answer manually GEOMETRIC MEANS
step by step
[tex]18 \sqrt{2} = \sqrt{3} .r ^{4 - 1}[/tex]


Sagot :

Given the equation:

[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]

This simplifies the expression:

[tex]\frac{18\sqrt{6}}{3}[/tex]

[tex]6\sqrt{6}[/tex]

So we now have:

[tex]r^3 = 6\sqrt{6}[/tex]

Step 4: Solve for ( r )

The value of ( r ) is:

[tex]r = \sqrt[3]{6\sqrt{6}}[/tex]