Solve sqrt{(8-15)^2+(5+2)^2}

$$\sqrt { ( 8 - 15 ) ^ { 2 } + ( 5 + 2 ) ^ { 2 } }$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

Solution Steps

Subtract 15 from 8 to get -7.

$$\sqrt{\left(-7\right)^{2}+\left(5+2\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\sqrt{49+\left(5+2\right)^{2}}$$

Add 5 and 2 to get 7.

$$\sqrt{49+7^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\sqrt{49+49}$$

Add 49 and 49 to get 98.

$$\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$7\sqrt{2}$$