Solve sqrt{48^2+72^2+162^2}

$$\sqrt { 48 ^ { 2 } + 72 ^ { 2 } + 162 ^ { 2 } }$$

Evaluate

$$6\sqrt{937}\approx 183.66273438$$

Solution Steps

Calculate 48 to the power of 2 and get 2304.

$$\sqrt{2304+72^{2}+162^{2}}$$

Calculate 72 to the power of 2 and get 5184.

$$\sqrt{2304+5184+162^{2}}$$

Add 2304 and 5184 to get 7488.

$$\sqrt{7488+162^{2}}$$

Calculate 162 to the power of 2 and get 26244.

$$\sqrt{7488+26244}$$

Add 7488 and 26244 to get 33732.

$$\sqrt{33732}$$

Factor 33732=6^{2}\times 937. Rewrite the square root of the product \sqrt{6^{2}\times 937} as the product of square roots \sqrt{6^{2}}\sqrt{937}. Take the square root of 6^{2}.

$$6\sqrt{937}$$