Solve sqrt{118/27+19/27}

$$\sqrt { 1 \frac { 18 } { 27 } + \frac { 19 } { 27 } }$$

Evaluate

$$\frac{8\sqrt{3}}{9}\approx 1.539600718$$

Solution Steps

Multiply 1 and 27 to get 27.

$$\sqrt{\frac{27+18}{27}+\frac{19}{27}}$$

Add 27 and 18 to get 45.

$$\sqrt{\frac{45}{27}+\frac{19}{27}}$$

Since \frac{45}{27} and \frac{19}{27} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{45+19}{27}}$$

Add 45 and 19 to get 64.

$$\sqrt{\frac{64}{27}}$$

Rewrite the square root of the division \sqrt{\frac{64}{27}} as the division of square roots \frac{\sqrt{64}}{\sqrt{27}}.

$$\frac{\sqrt{64}}{\sqrt{27}}$$

Calculate the square root of 64 and get 8.

$$\frac{8}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{8}{3\sqrt{3}}$$

Rationalize the denominator of \frac{8}{3\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{8\sqrt{3}}{3\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{8\sqrt{3}}{3\times 3}$$

Multiply 3 and 3 to get 9.

$$\frac{8\sqrt{3}}{9}$$