Solve sqrt{36+256/3}

$$\sqrt { 36 + \frac { 256 } { 3 } }$$

Evaluate

$$\frac{2\sqrt{273}}{3}\approx 11.015141095$$

Solution Steps

Convert 36 to fraction \frac{108}{3}.

$$\sqrt{\frac{108}{3}+\frac{256}{3}}$$

Since \frac{108}{3} and \frac{256}{3} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{108+256}{3}}$$

Add 108 and 256 to get 364.

$$\sqrt{\frac{364}{3}}$$

Rewrite the square root of the division \sqrt{\frac{364}{3}} as the division of square roots \frac{\sqrt{364}}{\sqrt{3}}.

$$\frac{\sqrt{364}}{\sqrt{3}}$$

Factor 364=2^{2}\times 91. Rewrite the square root of the product \sqrt{2^{2}\times 91} as the product of square roots \sqrt{2^{2}}\sqrt{91}. Take the square root of 2^{2}.

$$\frac{2\sqrt{91}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{91}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{91}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{91}\sqrt{3}}{3}$$

To multiply \sqrt{91} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{273}}{3}$$