Solve sqrt{8}sqrt{6}-3sqrt{6}sqrt{3}+2sqrt{12}-sqrt{72}

$$\sqrt{ 8 } \sqrt{ 6 } -3 \sqrt{ 6 } \sqrt{ 3 } +2 \sqrt{ 12 } - \sqrt{ 72 }$$

Evaluate

$$8\sqrt{3}-15\sqrt{2}\approx -7.356796975$$

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}.

$$2\sqrt{2}\sqrt{6}-3\sqrt{6}\sqrt{3}+2\sqrt{12}-\sqrt{72}$$

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}.

$$2\sqrt{2}\sqrt{2}\sqrt{3}-3\sqrt{6}\sqrt{3}+2\sqrt{12}-\sqrt{72}$$

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

$$2\times 2\sqrt{3}-3\sqrt{6}\sqrt{3}+2\sqrt{12}-\sqrt{72}$$

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}.

$$2\times 2\sqrt{3}-3\sqrt{3}\sqrt{2}\sqrt{3}+2\sqrt{12}-\sqrt{72}$$

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

$$2\times 2\sqrt{3}-3\times 3\sqrt{2}+2\sqrt{12}-\sqrt{72}$$

Multiply 3 and 3 to get 9.

$$2\times 2\sqrt{3}-9\sqrt{2}+2\sqrt{12}-\sqrt{72}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\times 2\sqrt{3}-9\sqrt{2}+2\times 2\sqrt{3}-\sqrt{72}$$

Multiply 2 and 2 to get 4.

$$2\times 2\sqrt{3}-9\sqrt{2}+4\sqrt{3}-\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$2\times 2\sqrt{3}-9\sqrt{2}+4\sqrt{3}-6\sqrt{2}$$

Combine -9\sqrt{2} and -6\sqrt{2} to get -15\sqrt{2}.

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

Multiply 2 and 2 to get 4.

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

Combine 4\sqrt{3} and 4\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}-15\sqrt{2}$$