Solve sqrt{{left(-15/3-10/5right)}^2}+sqrt{{left(20/3-13/2right)}^2}

$$\sqrt{ { \left( \frac{ -15 }{ 3 } - \frac{ 10 }{ 5 } \right) }^{ 2 } } + \sqrt{ { \left( \frac{ 20 }{ 3 } - \frac{ 13 }{ 2 } \right) }^{ 2 } }$$

Evaluate

$$\frac{43}{6}\approx 7.166666667$$

Solution Steps

Divide -15 by 3 to get -5.

$$\sqrt{\left(-5-\frac{10}{5}\right)^{2}}+\sqrt{\left(\frac{20}{3}-\frac{13}{2}\right)^{2}}$$

Divide 10 by 5 to get 2.

$$\sqrt{\left(-5-2\right)^{2}}+\sqrt{\left(\frac{20}{3}-\frac{13}{2}\right)^{2}}$$

Subtract 2 from -5 to get -7.

$$\sqrt{\left(-7\right)^{2}}+\sqrt{\left(\frac{20}{3}-\frac{13}{2}\right)^{2}}$$

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

$$\sqrt{49}+\sqrt{\left(\frac{20}{3}-\frac{13}{2}\right)^{2}}$$

Calculate the square root of 49 and get 7.

$$7+\sqrt{\left(\frac{20}{3}-\frac{13}{2}\right)^{2}}$$

Subtract \frac{13}{2} from \frac{20}{3} to get \frac{1}{6}.

$$7+\sqrt{\left(\frac{1}{6}\right)^{2}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$7+\sqrt{\frac{1}{36}}$$

Rewrite the square root of the division \frac{1}{36} as the division of square roots \frac{\sqrt{1}}{\sqrt{36}}. Take the square root of both numerator and denominator.

$$7+\frac{1}{6}$$

Add 7 and \frac{1}{6} to get \frac{43}{6}.

$$\frac{43}{6}$$

Factor

$$\frac{43}{2 \cdot 3} = 7\frac{1}{6} = 7.166666666666667$$