Solve 5sqrt{8}-sqrt{27}-sqrt{32}+3sqrt{3}+sqrt{2}=

$$5 \sqrt{ 8 } - \sqrt{ 27 } - \sqrt{ 32 } +3 \sqrt{ 3 } + \sqrt{ 2 } =$$

Evaluate

$$7\sqrt{2}\approx 9.899494937$$

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}.

$$5\times 2\sqrt{2}-\sqrt{27}-\sqrt{32}+3\sqrt{3}+\sqrt{2}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{2}-\sqrt{27}-\sqrt{32}+3\sqrt{3}+\sqrt{2}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$10\sqrt{2}-3\sqrt{3}-\sqrt{32}+3\sqrt{3}+\sqrt{2}$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Combine 10\sqrt{2} and -4\sqrt{2} to get 6\sqrt{2}.

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

Combine -3\sqrt{3} and 3\sqrt{3} to get 0.

$$6\sqrt{2}+\sqrt{2}$$

Combine 6\sqrt{2} and \sqrt{2} to get 7\sqrt{2}.

$$7\sqrt{2}$$