Solve x=8+9sqrt{26/3}

$$x=8+9 \sqrt{ \frac{ 26 }{ 3 } }$$

Solve for x

$$x=3\sqrt{78}+8\approx 34.495282599$$

Steps for Solving Linear Equation

Rewrite the square root of the division \sqrt{\frac{26}{3}} as the division of square roots \frac{\sqrt{26}}{\sqrt{3}}.

$$x=8+9\times \frac{\sqrt{26}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{26}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$x=8+9\times \frac{\sqrt{26}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$x=8+9\times \frac{\sqrt{26}\sqrt{3}}{3}$$

To multiply \sqrt{26} and \sqrt{3}, multiply the numbers under the square root.

$$x=8+9\times \frac{\sqrt{78}}{3}$$

Cancel out 3, the greatest common factor in 9 and 3.

$$x=8+3\sqrt{78}$$

Assign x

$$x≔3\sqrt{78}+8$$