Solve for m square root of (9m)/2-6=0

$\sqrt{\frac{9 m}{2}} - 6 = 0$

Add $6$ to both sides of the equation.

$\sqrt{\frac{9 m}{2}} = 6$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{\frac{9 m}{2}}}^{2} = 6^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{9 m}{2}}$ as ${(\frac{9 m}{2})}^{\frac{1}{2}}$ .

${({(\frac{9 m}{2})}^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${({(\frac{9 m}{2})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{9 m}{2})}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{9 m}{2})}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{9 m}{2})}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

${(\frac{9 m}{2})}^{1} = 6^{2}$

Simplify.

$\frac{9 m}{2} = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$\frac{9 m}{2} = 36$

Solve for $m$ .

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} \cdot \frac{9 m}{2} = \frac{2}{9} \cdot 36$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{9} \cdot \frac{9 m}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 m}{2} = \frac{2}{9} \cdot 36$

Rewrite the expression.

$\frac{1}{9} (9 m) = \frac{2}{9} \cdot 36$

Cancel the common factor of $9$ .

Factor $9$ out of $9 m$ .

$\frac{1}{9} (9 (m)) = \frac{2}{9} \cdot 36$

Cancel the common factor.

$\frac{1}{9} (9 m) = \frac{2}{9} \cdot 36$

Rewrite the expression.

$m = \frac{2}{9} \cdot 36$

Simplify the right side.

Simplify $\frac{2}{9} \cdot 36$ .

Cancel the common factor of $9$ .

Factor $9$ out of $36$ .

$m = \frac{2}{9} \cdot (9 (4))$

Cancel the common factor.

$m = \frac{2}{9} \cdot (9 \cdot 4)$

Rewrite the expression.

$m = 2 \cdot 4$

Multiply $2$ by $4$ .

$m = 8$

Solve for m square root of (9m)/2-6=0

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