Solve (2)-sqrt[3]{155/8}*sqrt{4/25}:quad(3)sqrt[3]{27}+(-sqrt{0.64})*sqrt{400}

$$( 2 ) - \sqrt[ 3 ] { 15 \frac { 5 } { 8 } } \times \sqrt { \frac { 4 } { 25 } } : \quad ( 3 ) \sqrt[ 3 ] { 27 } + ( - \sqrt { 0.64 } ) \times \sqrt { 400 }$$

Evaluate

$$-15$$

Solution Steps

Multiply 15 and 8 to get 120.

$$2-\frac{\sqrt[3]{\frac{120+5}{8}}\sqrt{\frac{4}{25}}}{3}\sqrt[3]{27}+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Add 120 and 5 to get 125.

$$2-\frac{\sqrt[3]{\frac{125}{8}}\sqrt{\frac{4}{25}}}{3}\sqrt[3]{27}+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Calculate \sqrt[3]{\frac{125}{8}} and get \frac{5}{2}.

$$2-\frac{\frac{5}{2}\sqrt{\frac{4}{25}}}{3}\sqrt[3]{27}+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Rewrite the square root of the division \frac{4}{25} as the division of square roots \frac{\sqrt{4}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$2-\frac{\frac{5}{2}\times \frac{2}{5}}{3}\sqrt[3]{27}+\left(-\sqrt{0.64}\right)\sqrt{400}$$

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

$$2-\frac{1}{3}\sqrt[3]{27}+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Calculate \sqrt[3]{27} and get 3.

$$2-\frac{1}{3}\times 3+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Multiply \frac{1}{3} and 3 to get 1.

$$2-1+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Subtract 1 from 2 to get 1.

$$1+\left(-\sqrt{0.64}\right)\sqrt{400}$$

Calculate the square root of 0.64 and get 0.8.

$$1-0.8\sqrt{400}$$

Calculate the square root of 400 and get 20.

$$1-0.8\times 20$$

Multiply -0.8 and 20 to get -16.

$$1-16$$

Subtract 16 from 1 to get -15.

$$-15$$

Factor

$$-15$$