Solve 1/2sqrt{5}*sqrt{5}*sqrt{(sqrt{7})^2}+(-sqrt{2})^2

$$\frac { 1 } { 2 } \sqrt { 5 } \times \sqrt { 5 } \times \sqrt { ( \sqrt { 7 } ) ^ { 2 } } + ( - \sqrt { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{5\sqrt{7}}{2}+2\approx 8.614378278$$

Solution Steps

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{1}{2}\times 5\sqrt{\left(\sqrt{7}\right)^{2}}+\left(-\sqrt{2}\right)^{2}$$

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

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

The square of \sqrt{7} is 7.

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

Calculate -\sqrt{2} to the power of 2 and get \left(\sqrt{2}\right)^{2}.

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

The square of \sqrt{2} is 2.

$$\frac{5}{2}\sqrt{7}+2$$

Factor

$$\frac{5 \sqrt{7} + 4}{2} = 8.614378277661476$$