Solve sqrt{{left(17sqrt{3}right)}^2+{left(17sqrt{3}right)}^2}

$$\sqrt{ { \left(17 \sqrt{ 3 } \right) }^{ 2 } + { \left(17 \sqrt{ 3 } \right) }^{ 2 } }$$

Evaluate

$$17\sqrt{6}\approx 41.641325627$$

Solution Steps

Expand \left(17\sqrt{3}\right)^{2}.

$$\sqrt{17^{2}\left(\sqrt{3}\right)^{2}+\left(17\sqrt{3}\right)^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$\sqrt{289\left(\sqrt{3}\right)^{2}+\left(17\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{289\times 3+\left(17\sqrt{3}\right)^{2}}$$

Multiply 289 and 3 to get 867.

$$\sqrt{867+\left(17\sqrt{3}\right)^{2}}$$

Expand \left(17\sqrt{3}\right)^{2}.

$$\sqrt{867+17^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$\sqrt{867+289\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{867+289\times 3}$$

Multiply 289 and 3 to get 867.

$$\sqrt{867+867}$$

Add 867 and 867 to get 1734.

$$\sqrt{1734}$$

Factor 1734=17^{2}\times 6. Rewrite the square root of the product \sqrt{17^{2}\times 6} as the product of square roots \sqrt{17^{2}}\sqrt{6}. Take the square root of 17^{2}.

$$17\sqrt{6}$$