Solve (2sqrt{3})-(3sqrt{2})(3sqrt{8})

$$( 2 \sqrt { 3 } ) - ( 3 \sqrt { 2 } ) ( 3 \sqrt { 8 } )$$

Evaluate

$$2\left(\sqrt{3}-18\right)\approx -32.535898385$$

Solution Steps

Factor 8=2\times 4. Rewrite the square root of the product \sqrt{2\times 4} as the product of square roots \sqrt{2}\sqrt{4}.

$$2\sqrt{3}-3\sqrt{2}\times 3\sqrt{2}\sqrt{4}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2\sqrt{3}-3\times 2\times 3\sqrt{4}$$

Multiply 3 and 2 to get 6.

$$2\sqrt{3}-6\times 3\sqrt{4}$$

Multiply 6 and 3 to get 18.

$$2\sqrt{3}-18\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$2\sqrt{3}-18\times 2$$

Multiply 18 and 2 to get 36.

$$2\sqrt{3}-36$$

Factor

$$2 {(\sqrt{3} - 18)} = -32.535898385$$