Solve 2sqrt{8}-3sqrt{10}*sqrt{8}-6sqrt{10}+3sqrt{5}

$$2 \sqrt{ 8 } -3 \sqrt{ 10 } \times \sqrt{ 8 } -6 \sqrt{ 10 } +3 \sqrt{ 5 }$$

Evaluate

$$4\sqrt{2}-6\sqrt{10}-9\sqrt{5}\approx -33.441423509$$

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}.

$$2\times 2\sqrt{2}-3\sqrt{10}\sqrt{8}-6\sqrt{10}+3\sqrt{5}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}-3\sqrt{10}\sqrt{8}-6\sqrt{10}+3\sqrt{5}$$

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}.

$$4\sqrt{2}-3\sqrt{10}\times 2\sqrt{2}-6\sqrt{10}+3\sqrt{5}$$

Multiply 3 and 2 to get 6.

$$4\sqrt{2}-6\sqrt{10}\sqrt{2}-6\sqrt{10}+3\sqrt{5}$$

Factor 10=2\times 5. Rewrite the square root of the product \sqrt{2\times 5} as the product of square roots \sqrt{2}\sqrt{5}.

$$4\sqrt{2}-6\sqrt{2}\sqrt{5}\sqrt{2}-6\sqrt{10}+3\sqrt{5}$$

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

$$4\sqrt{2}-6\times 2\sqrt{5}-6\sqrt{10}+3\sqrt{5}$$

Multiply 6 and 2 to get 12.

$$4\sqrt{2}-12\sqrt{5}-6\sqrt{10}+3\sqrt{5}$$

Combine -12\sqrt{5} and 3\sqrt{5} to get -9\sqrt{5}.

$$4\sqrt{2}-9\sqrt{5}-6\sqrt{10}$$