Solve (-8sqrt{1/4}+frac{sqrt{1,44}}{3}*sqrt{12,25}):(0,1sqrt{13})^2

$$( - 8 \sqrt { \frac { 1 } { 4 } } + \frac { \sqrt { 1,44 } } { 3 } \cdot \sqrt { 12,25 } ) : ( 0,1 \sqrt { 13 } ) ^ { 2 }$$

Evaluate

$$-20$$

Solution Steps

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{-8\times \frac{1}{2}+\frac{\sqrt{1,44}}{3}\sqrt{12,25}}{\left(0,1\sqrt{13}\right)^{2}}$$

Multiply -8 and \frac{1}{2} to get -4.

$$\frac{-4+\frac{\sqrt{1,44}}{3}\sqrt{12,25}}{\left(0,1\sqrt{13}\right)^{2}}$$

Calculate the square root of 1,44 and get 1,2.

$$\frac{-4+\frac{1,2}{3}\sqrt{12,25}}{\left(0,1\sqrt{13}\right)^{2}}$$

Expand \frac{1,2}{3} by multiplying both numerator and the denominator by 10.

$$\frac{-4+\frac{12}{30}\sqrt{12,25}}{\left(0,1\sqrt{13}\right)^{2}}$$

Reduce the fraction \frac{12}{30} to lowest terms by extracting and canceling out 6.

$$\frac{-4+\frac{2}{5}\sqrt{12,25}}{\left(0,1\sqrt{13}\right)^{2}}$$

Calculate the square root of 12,25 and get 3,5.

$$\frac{-4+\frac{2}{5}\times 3,5}{\left(0,1\sqrt{13}\right)^{2}}$$

Multiply \frac{2}{5} and 3,5 to get \frac{7}{5}.

$$\frac{-4+\frac{7}{5}}{\left(0,1\sqrt{13}\right)^{2}}$$

Add -4 and \frac{7}{5} to get -\frac{13}{5}.

$$\frac{-\frac{13}{5}}{\left(0,1\sqrt{13}\right)^{2}}$$

Expand \left(0,1\sqrt{13}\right)^{2}.

$$\frac{-\frac{13}{5}}{0,1^{2}\left(\sqrt{13}\right)^{2}}$$

Calculate 0,1 to the power of 2 and get 0,01.

$$\frac{-\frac{13}{5}}{0,01\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{-\frac{13}{5}}{0,01\times 13}$$

Multiply 0,01 and 13 to get 0,13.

$$\frac{-\frac{13}{5}}{0,13}$$

Express \frac{-\frac{13}{5}}{0,13} as a single fraction.

$$\frac{-13}{5\times 0,13}$$

Multiply 5 and 0,13 to get 0,65.

$$\frac{-13}{0,65}$$

Expand \frac{-13}{0,65} by multiplying both numerator and the denominator by 100.

$$\frac{-1300}{65}$$

Divide -1300 by 65 to get -20.

$$-20$$

Factor

$$-20$$