Solve (6sqrt{3}-7sqrt{6})*(2sqrt{8}-3)

$$( 6 \sqrt { 3 } - 7 \sqrt { 6 } ) \cdot ( 2 \sqrt { 8 } - 3 )$$

Evaluate

$$45\sqrt{6}-74\sqrt{3}\approx -17.944721335$$

Solution Steps

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

$$\left(6\sqrt{3}-7\sqrt{6}\right)\left(2\times 2\sqrt{2}-3\right)$$

Multiply 2 and 2 to get 4.

$$\left(6\sqrt{3}-7\sqrt{6}\right)\left(4\sqrt{2}-3\right)$$

Apply the distributive property by multiplying each term of 6\sqrt{3}-7\sqrt{6} by each term of 4\sqrt{2}-3.

$$24\sqrt{3}\sqrt{2}-18\sqrt{3}-28\sqrt{6}\sqrt{2}+21\sqrt{6}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$24\sqrt{6}-18\sqrt{3}-28\sqrt{6}\sqrt{2}+21\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$24\sqrt{6}-18\sqrt{3}-28\sqrt{2}\sqrt{3}\sqrt{2}+21\sqrt{6}$$

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

$$24\sqrt{6}-18\sqrt{3}-28\times 2\sqrt{3}+21\sqrt{6}$$

Multiply -28 and 2 to get -56.

$$24\sqrt{6}-18\sqrt{3}-56\sqrt{3}+21\sqrt{6}$$

Combine -18\sqrt{3} and -56\sqrt{3} to get -74\sqrt{3}.

$$24\sqrt{6}-74\sqrt{3}+21\sqrt{6}$$

Combine 24\sqrt{6} and 21\sqrt{6} to get 45\sqrt{6}.

$$45\sqrt{6}-74\sqrt{3}$$

Factor

$$45 \sqrt{6} - 74 \sqrt{3} = -17.944721335$$