Solve sqrt{(2sqrt{6})^2+6^2}

$$\sqrt { ( 2 \sqrt { 6 } ) ^ { 2 } + 6 ^ { 2 } }$$

Evaluate

$$2\sqrt{15}\approx 7.745966692$$

Solution Steps

Expand \left(2\sqrt{6}\right)^{2}.

$$\sqrt{2^{2}\left(\sqrt{6}\right)^{2}+6^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4\left(\sqrt{6}\right)^{2}+6^{2}}$$

The square of \sqrt{6} is 6.

$$\sqrt{4\times 6+6^{2}}$$

Multiply 4 and 6 to get 24.

$$\sqrt{24+6^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{24+36}$$

Add 24 and 36 to get 60.

$$\sqrt{60}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$2\sqrt{15}$$