Solve sqrt[3]{9sqrt{3}-11sqrt{2}}=sqrt{3}+ksqrt{2}

$$\sqrt[ 3 ] { 9 \sqrt { 3 } - 11 \sqrt { 2 } } = \sqrt { 3 } + k \sqrt { 2 }$$

Solve for k

$$k = -\frac{\sqrt{2} {(-\sqrt[3]{9 \sqrt{3} - 11 \sqrt{2}} + \sqrt{3})}}{2} \approx -1$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{3}+k\sqrt{2}=\sqrt[3]{9\sqrt{3}-11\sqrt{2}}$$

Subtract \sqrt{3} from both sides.

$$k\sqrt{2}=\sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3}$$

The equation is in standard form.

$$\sqrt{2}k=\sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3}$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}k}{\sqrt{2}}=\frac{\sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3}}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$k=\frac{\sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3}}{\sqrt{2}}$$

Divide \sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3} by \sqrt{2}.

$$k=\frac{\sqrt{2}\left(\sqrt[3]{9\sqrt{3}-11\sqrt{2}}-\sqrt{3}\right)}{2}$$