Solve sqrt{left(79-145right)^2+left(194-198right)^2+left(225-235right)^2}

$$\sqrt{ { \left( 79-145 \right) }^{ 2 } + { \left( 194-198 \right) }^{ 2 } + { \left( 225-235 \right) }^{ 2 } }$$

Evaluate

$$2\sqrt{1118}\approx 66.873013989$$

Solution Steps

Subtract 145 from 79 to get -66.

$$\sqrt{\left(-66\right)^{2}+\left(194-198\right)^{2}+\left(225-235\right)^{2}}$$

Calculate -66 to the power of 2 and get 4356.

$$\sqrt{4356+\left(194-198\right)^{2}+\left(225-235\right)^{2}}$$

Subtract 198 from 194 to get -4.

$$\sqrt{4356+\left(-4\right)^{2}+\left(225-235\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$\sqrt{4356+16+\left(225-235\right)^{2}}$$

Add 4356 and 16 to get 4372.

$$\sqrt{4372+\left(225-235\right)^{2}}$$

Subtract 235 from 225 to get -10.

$$\sqrt{4372+\left(-10\right)^{2}}$$

Calculate -10 to the power of 2 and get 100.

$$\sqrt{4372+100}$$

Add 4372 and 100 to get 4472.

$$\sqrt{4472}$$

Factor 4472=2^{2}\times 1118. Rewrite the square root of the product \sqrt{2^{2}\times 1118} as the product of square roots \sqrt{2^{2}}\sqrt{1118}. Take the square root of 2^{2}.

$$2\sqrt{1118}$$