Solve sqrt{(5+1)^2+(-5+9)^2}

$$\sqrt { ( 5 + 1 ) ^ { 2 } + ( - 5 + 9 ) ^ { 2 } }$$

Evaluate

$$2\sqrt{13}\approx 7.211102551$$

Solution Steps

Add 5 and 1 to get 6.

$$\sqrt{6^{2}+\left(-5+9\right)^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36+\left(-5+9\right)^{2}}$$

Add -5 and 9 to get 4.

$$\sqrt{36+4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\sqrt{36+16}$$

Add 36 and 16 to get 52.

$$\sqrt{52}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$2\sqrt{13}$$