Solve -1/4*({left(frac{5sqrt{10}-8}{3}right)}^2

$$- \frac{ 1 }{ 4 } \times ( { \left( \frac{ 5 \sqrt{ 10 } -8 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{20\sqrt{10}}{9}-\frac{157}{18}\approx -1.694938533$$

Solution Steps

To raise \frac{5\sqrt{10}-8}{3} to a power, raise both numerator and denominator to the power and then divide.

$$-\frac{1}{4}\times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}}$$

Multiply -\frac{1}{4} times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(5\sqrt{10}-8\right)^{2}}{4\times 3^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{10}-8\right)^{2}.

$$\frac{-\left(25\left(\sqrt{10}\right)^{2}-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{-\left(25\times 10-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Multiply 25 and 10 to get 250.

$$\frac{-\left(250-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Add 250 and 64 to get 314.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 9}$$

Multiply 4 and 9 to get 36.

$$\frac{-\left(314-80\sqrt{10}\right)}{36}$$

To find the opposite of 314-80\sqrt{10}, find the opposite of each term.

$$\frac{-314+80\sqrt{10}}{36}$$

Expand

$$\frac{20 \sqrt{10}}{9} - \frac{157}{18} = -1.694938533$$

Solution Steps

To raise \frac{5\sqrt{10}-8}{3} to a power, raise both numerator and denominator to the power and then divide.

$$-\frac{1}{4}\times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}}$$

Multiply -\frac{1}{4} times \frac{\left(5\sqrt{10}-8\right)^{2}}{3^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(5\sqrt{10}-8\right)^{2}}{4\times 3^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{10}-8\right)^{2}.

$$\frac{-\left(25\left(\sqrt{10}\right)^{2}-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{-\left(25\times 10-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Multiply 25 and 10 to get 250.

$$\frac{-\left(250-80\sqrt{10}+64\right)}{4\times 3^{2}}$$

Add 250 and 64 to get 314.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\left(314-80\sqrt{10}\right)}{4\times 9}$$

Multiply 4 and 9 to get 36.

$$\frac{-\left(314-80\sqrt{10}\right)}{36}$$

To find the opposite of 314-80\sqrt{10}, find the opposite of each term.

$$\frac{-314+80\sqrt{10}}{36}$$