Solve frac{sqrt{100+26^2+32^2}}{3}

$$\frac { \sqrt { 100 + 26 ^ { 2 } + 32 ^ { 2 } } } { 3 }$$

Evaluate

$$10\sqrt{2}\approx 14.142135624$$

Solution Steps

Calculate 26 to the power of 2 and get 676.

$$\frac{\sqrt{100+676+32^{2}}}{3}$$

Add 100 and 676 to get 776.

$$\frac{\sqrt{776+32^{2}}}{3}$$

Calculate 32 to the power of 2 and get 1024.

$$\frac{\sqrt{776+1024}}{3}$$

Add 776 and 1024 to get 1800.

$$\frac{\sqrt{1800}}{3}$$

Factor 1800=30^{2}\times 2. Rewrite the square root of the product \sqrt{30^{2}\times 2} as the product of square roots \sqrt{30^{2}}\sqrt{2}. Take the square root of 30^{2}.

$$\frac{30\sqrt{2}}{3}$$

Divide 30\sqrt{2} by 3 to get 10\sqrt{2}.

$$10\sqrt{2}$$