Solve sqrt{14^2+14^2+14^2}

$$\sqrt { 14 ^ { 2 } + 14 ^ { 2 } + 14 ^ { 2 } }$$

Evaluate

$$14\sqrt{3}\approx 24.248711306$$

Solution Steps

Calculate 14 to the power of 2 and get 196.

$$\sqrt{196+14^{2}+14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\sqrt{196+196+14^{2}}$$

Add 196 and 196 to get 392.

$$\sqrt{392+14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\sqrt{392+196}$$

Add 392 and 196 to get 588.

$$\sqrt{588}$$

Factor 588=14^{2}\times 3. Rewrite the square root of the product \sqrt{14^{2}\times 3} as the product of square roots \sqrt{14^{2}}\sqrt{3}. Take the square root of 14^{2}.

$$14\sqrt{3}$$