Solve sqrt{(-3)^2}-(-sqrt{20})^2*sqrt{(4/5)^2}

$$\sqrt { ( - 3 ) ^ { 2 } } - ( - \sqrt { 20 } ) ^ { 2 } \times \sqrt { ( \frac { 4 } { 5 } ) ^ { 2 } }$$

Evaluate

$$-13$$

Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\sqrt{9}-\left(-\sqrt{20}\right)^{2}\sqrt{\left(\frac{4}{5}\right)^{2}}$$

Calculate the square root of 9 and get 3.

$$3-\left(-\sqrt{20}\right)^{2}\sqrt{\left(\frac{4}{5}\right)^{2}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Calculate -2\sqrt{5} to the power of 2 and get \left(2\sqrt{5}\right)^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

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

Multiply 4 and 5 to get 20.

$$3-20\sqrt{\left(\frac{4}{5}\right)^{2}}$$

Calculate \frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$3-20\sqrt{\frac{16}{25}}$$

Rewrite the square root of the division \frac{16}{25} as the division of square roots \frac{\sqrt{16}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$3-20\times \frac{4}{5}$$

Multiply 20 and \frac{4}{5} to get 16.

$$3-16$$

Subtract 16 from 3 to get -13.

$$-13$$

Factor

$$-13$$