Solve sqrt{(53-5)^2+(2-53)^2}

$$\sqrt { ( 53 - 5 ) ^ { 2 } + ( 2 - 53 ) ^ { 2 } }$$

Evaluate

$$3\sqrt{545}\approx 70.03570518$$

Solution Steps

Subtract 5 from 53 to get 48.

$$\sqrt{48^{2}+\left(2-53\right)^{2}}$$

Calculate 48 to the power of 2 and get 2304.

$$\sqrt{2304+\left(2-53\right)^{2}}$$

Subtract 53 from 2 to get -51.

$$\sqrt{2304+\left(-51\right)^{2}}$$

Calculate -51 to the power of 2 and get 2601.

$$\sqrt{2304+2601}$$

Add 2304 and 2601 to get 4905.

$$\sqrt{4905}$$

Factor 4905=3^{2}\times 545. Rewrite the square root of the product \sqrt{3^{2}\times 545} as the product of square roots \sqrt{3^{2}}\sqrt{545}. Take the square root of 3^{2}.

$$3\sqrt{545}$$