Solve frac{sqrt{4}*sqrt{20}}{sqrt{5}}+(frac{0,5sqrt{5}+sqrt{5}}{6})^2j

$$\frac { \sqrt { 4 } \cdot \sqrt { 20 } } { \sqrt { 5 } } + ( \frac { 0,5 \sqrt { 5 } + \sqrt { 5 } } { 6 } ) ^ { 2 } j$$

Evaluate

$$\frac{5j}{16}+4$$

Solution Steps

Factor 20=4\times 5. Rewrite the square root of the product \sqrt{4\times 5} as the product of square roots \sqrt{4}\sqrt{5}.

$$\frac{\sqrt{4}\sqrt{4}\sqrt{5}}{\sqrt{5}}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

Multiply \sqrt{4} and \sqrt{4} to get 4.

$$\frac{4\sqrt{5}}{\sqrt{5}}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

Rationalize the denominator of \frac{4\sqrt{5}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4\sqrt{5}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

The square of \sqrt{5} is 5.

$$\frac{4\sqrt{5}\sqrt{5}}{5}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

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

$$\frac{4\times 5}{5}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

Multiply 4 and 5 to get 20.

$$\frac{20}{5}+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

Divide 20 by 5 to get 4.

$$4+\left(\frac{0,5\sqrt{5}+\sqrt{5}}{6}\right)^{2}j$$

Combine 0,5\sqrt{5} and \sqrt{5} to get 1,5\sqrt{5}.

$$4+\left(\frac{1,5\sqrt{5}}{6}\right)^{2}j$$

Divide 1,5\sqrt{5} by 6 to get 0,25\sqrt{5}.

$$4+\left(0,25\sqrt{5}\right)^{2}j$$

Expand \left(0,25\sqrt{5}\right)^{2}.

$$4+0,25^{2}\left(\sqrt{5}\right)^{2}j$$

Calculate 0,25 to the power of 2 and get 0,0625.

$$4+0,0625\left(\sqrt{5}\right)^{2}j$$

The square of \sqrt{5} is 5.

$$4+0,0625\times 5j$$

Multiply 0,0625 and 5 to get 0,3125.

$$4+0,3125j$$

Factor

$$\frac{5j+64}{16}$$