Solve sqrt{(4sqrt{5})^2+4^2}

$$\sqrt { ( 4 \sqrt { 5 } ) ^ { 2 } + 4 ^ { 2 } }$$

Evaluate

$$4\sqrt{6}\approx 9.797958971$$

Solution Steps

Expand \left(4\sqrt{5}\right)^{2}.

$$\sqrt{4^{2}\left(\sqrt{5}\right)^{2}+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{16\left(\sqrt{5}\right)^{2}+4^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{16\times 5+4^{2}}$$

Multiply 16 and 5 to get 80.

$$\sqrt{80+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{80+16}$$

Add 80 and 16 to get 96.

$$\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$4\sqrt{6}$$