Solve sqrt{{left(16sqrt{5}right)}^2+{left(frac{16sqrt{5}}{2}right)}^2}

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

Evaluate

$$40$$

Solution Steps

Expand \left(16\sqrt{5}\right)^{2}.

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

Calculate 16 to the power of 2 and get 256.

$$\sqrt{256\left(\sqrt{5}\right)^{2}+\left(\frac{16\sqrt{5}}{2}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{256\times 5+\left(\frac{16\sqrt{5}}{2}\right)^{2}}$$

Multiply 256 and 5 to get 1280.

$$\sqrt{1280+\left(\frac{16\sqrt{5}}{2}\right)^{2}}$$

Divide 16\sqrt{5} by 2 to get 8\sqrt{5}.

$$\sqrt{1280+\left(8\sqrt{5}\right)^{2}}$$

Expand \left(8\sqrt{5}\right)^{2}.

$$\sqrt{1280+8^{2}\left(\sqrt{5}\right)^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\sqrt{1280+64\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\sqrt{1280+64\times 5}$$

Multiply 64 and 5 to get 320.

$$\sqrt{1280+320}$$

Add 1280 and 320 to get 1600.

$$\sqrt{1600}$$

Calculate the square root of 1600 and get 40.

$$40$$

Factor

$$2^{3}\times 5$$