Solve 3sqrt{2}*(2-sqrt{3})-7*(4-2sqrt{2})-2*(5sqrt{3}-2sqrt{2})=

$$3 \sqrt { 2 } \cdot ( 2 - \sqrt { 3 } ) - 7 \cdot ( 4 - 2 \sqrt { 2 } ) - 2 \cdot ( 5 \sqrt { 3 } - 2 \sqrt { 2 } ) =$$

Evaluate

$$24\sqrt{2}-3\sqrt{6}-10\sqrt{3}-28\approx -18.727851807$$

Solution Steps

Use the distributive property to multiply 3\sqrt{2} by 2-\sqrt{3}.

$$6\sqrt{2}-3\sqrt{3}\sqrt{2}-7\left(4-2\sqrt{2}\right)-2\left(5\sqrt{3}-2\sqrt{2}\right)$$

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

$$6\sqrt{2}-3\sqrt{6}-7\left(4-2\sqrt{2}\right)-2\left(5\sqrt{3}-2\sqrt{2}\right)$$

Use the distributive property to multiply -7 by 4-2\sqrt{2}.

$$6\sqrt{2}-3\sqrt{6}-28+14\sqrt{2}-2\left(5\sqrt{3}-2\sqrt{2}\right)$$

Combine 6\sqrt{2} and 14\sqrt{2} to get 20\sqrt{2}.

$$20\sqrt{2}-3\sqrt{6}-28-2\left(5\sqrt{3}-2\sqrt{2}\right)$$

Use the distributive property to multiply -2 by 5\sqrt{3}-2\sqrt{2}.

$$20\sqrt{2}-3\sqrt{6}-28-10\sqrt{3}+4\sqrt{2}$$

Combine 20\sqrt{2} and 4\sqrt{2} to get 24\sqrt{2}.

$$24\sqrt{2}-3\sqrt{6}-28-10\sqrt{3}$$