Solve sqrt{2}*sqrt{2}*sqrt{8}+(5*sqrt{6}-7*sqrt{8})*sqrt{3}=

$$\sqrt { 2 } \cdot \sqrt { 2 } \cdot \sqrt { 8 } + ( 5 \cdot \sqrt { 6 } - 7 \cdot \sqrt { 8 } ) \cdot \sqrt { 3 } =$$

Evaluate

$$19\sqrt{2}-14\sqrt{6}\approx -7.422798714$$

Solution Steps

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

$$2\sqrt{8}+\left(5\sqrt{6}-7\sqrt{8}\right)\sqrt{3}$$

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}.

$$2\times 2\sqrt{2}+\left(5\sqrt{6}-7\sqrt{8}\right)\sqrt{3}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}+\left(5\sqrt{6}-7\sqrt{8}\right)\sqrt{3}$$

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}.

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

Multiply -7 and 2 to get -14.

$$4\sqrt{2}+\left(5\sqrt{6}-14\sqrt{2}\right)\sqrt{3}$$

Use the distributive property to multiply 5\sqrt{6}-14\sqrt{2} by \sqrt{3}.

$$4\sqrt{2}+5\sqrt{6}\sqrt{3}-14\sqrt{2}\sqrt{3}$$

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

$$4\sqrt{2}+5\sqrt{3}\sqrt{2}\sqrt{3}-14\sqrt{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$4\sqrt{2}+5\times 3\sqrt{2}-14\sqrt{2}\sqrt{3}$$

Multiply 5 and 3 to get 15.

$$4\sqrt{2}+15\sqrt{2}-14\sqrt{2}\sqrt{3}$$

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

$$4\sqrt{2}+15\sqrt{2}-14\sqrt{6}$$

Combine 4\sqrt{2} and 15\sqrt{2} to get 19\sqrt{2}.

$$19\sqrt{2}-14\sqrt{6}$$