Solve sqrt{(2sqrt{3})^2+16}

$$\sqrt { ( 2 \sqrt { 3 } ) ^ { 2 } + 16 }$$

Evaluate

$$2\sqrt{7}\approx 5.291502622$$

Solution Steps

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

$$\sqrt{2^{2}\left(\sqrt{3}\right)^{2}+16}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4\left(\sqrt{3}\right)^{2}+16}$$

The square of \sqrt{3} is 3.

$$\sqrt{4\times 3+16}$$

Multiply 4 and 3 to get 12.

$$\sqrt{12+16}$$

Add 12 and 16 to get 28.

$$\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$2\sqrt{7}$$