Solve sqrt{(3sqrt{13})^2-3^2}

$$\sqrt { ( 3 \sqrt { 13 } ) ^ { 2 } - 3 ^ { 2 } }$$

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Expand \left(3\sqrt{13}\right)^{2}.

$$\sqrt{3^{2}\left(\sqrt{13}\right)^{2}-3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\left(\sqrt{13}\right)^{2}-3^{2}}$$

The square of \sqrt{13} is 13.

$$\sqrt{9\times 13-3^{2}}$$

Multiply 9 and 13 to get 117.

$$\sqrt{117-3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{117-9}$$

Subtract 9 from 117 to get 108.

$$\sqrt{108}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}$$