Solve 1/3+9sqrt{3*9(13+9)^2-4sqrt6^2}

$$\frac { 1 } { 3 + 9 } \sqrt { 3 \cdot 9 ( 13 + 9 ) ^ { 2 } - 4 \sqrt { 6 } ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{3261}}{6}\approx 9.51752769$$

Solution Steps

Add 3 and 9 to get 12.

$$\frac{1}{12}\sqrt{3\times 9\left(13+9\right)^{2}-4\left(\sqrt{6}\right)^{2}}$$

Multiply 3 and 9 to get 27.

$$\frac{1}{12}\sqrt{27\left(13+9\right)^{2}-4\left(\sqrt{6}\right)^{2}}$$

Add 13 and 9 to get 22.

$$\frac{1}{12}\sqrt{27\times 22^{2}-4\left(\sqrt{6}\right)^{2}}$$

Calculate 22 to the power of 2 and get 484.

$$\frac{1}{12}\sqrt{27\times 484-4\left(\sqrt{6}\right)^{2}}$$

Multiply 27 and 484 to get 13068.

$$\frac{1}{12}\sqrt{13068-4\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{1}{12}\sqrt{13068-4\times 6}$$

Multiply 4 and 6 to get 24.

$$\frac{1}{12}\sqrt{13068-24}$$

Subtract 24 from 13068 to get 13044.

$$\frac{1}{12}\sqrt{13044}$$

Factor 13044=2^{2}\times 3261. Rewrite the square root of the product \sqrt{2^{2}\times 3261} as the product of square roots \sqrt{2^{2}}\sqrt{3261}. Take the square root of 2^{2}.

$$\frac{1}{12}\times 2\sqrt{3261}$$

Multiply \frac{1}{12} and 2 to get \frac{1}{6}.

$$\frac{1}{6}\sqrt{3261}$$