Solve sqrt{(10+2)^2+(100)^2}-sqrt{(8)^2+(100)^2}

$$\sqrt { ( 10 + 2 ) ^ { 2 } + ( 100 ) ^ { 2 } } - \sqrt { ( 8 ) ^ { 2 } + ( 100 ) ^ { 2 } }$$

Evaluate

$$4\left(\sqrt{634}-\sqrt{629}\right)\approx 0.397936864$$

Solution Steps

Add 10 and 2 to get 12.

$$\sqrt{12^{2}+100^{2}}-\sqrt{8^{2}+100^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\sqrt{144+100^{2}}-\sqrt{8^{2}+100^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$\sqrt{144+10000}-\sqrt{8^{2}+100^{2}}$$

Add 144 and 10000 to get 10144.

$$\sqrt{10144}-\sqrt{8^{2}+100^{2}}$$

Factor 10144=4^{2}\times 634. Rewrite the square root of the product \sqrt{4^{2}\times 634} as the product of square roots \sqrt{4^{2}}\sqrt{634}. Take the square root of 4^{2}.

$$4\sqrt{634}-\sqrt{8^{2}+100^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$4\sqrt{634}-\sqrt{64+100^{2}}$$

Calculate 100 to the power of 2 and get 10000.

$$4\sqrt{634}-\sqrt{64+10000}$$

Add 64 and 10000 to get 10064.

$$4\sqrt{634}-\sqrt{10064}$$

Factor 10064=4^{2}\times 629. Rewrite the square root of the product \sqrt{4^{2}\times 629} as the product of square roots \sqrt{4^{2}}\sqrt{629}. Take the square root of 4^{2}.

$$4\sqrt{634}-4\sqrt{629}$$

Factor

$$4 {(\sqrt{634} - \sqrt{629})} = 0.397936864$$