Solve 2sqrt{18}+5sqrt{72}-4sqrt{8}-sqrt{50}=

$$2 \sqrt { 18 } + 5 \sqrt { 72 } - 4 \sqrt { 8 } - \sqrt { 50 } =$$

Evaluate

$$23\sqrt{2}\approx 32.526911935$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$2\times 3\sqrt{2}+5\sqrt{72}-4\sqrt{8}-\sqrt{50}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{2}+5\sqrt{72}-4\sqrt{8}-\sqrt{50}$$

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}.

$$6\sqrt{2}+5\times 6\sqrt{2}-4\sqrt{8}-\sqrt{50}$$

Multiply 5 and 6 to get 30.

$$6\sqrt{2}+30\sqrt{2}-4\sqrt{8}-\sqrt{50}$$

Combine 6\sqrt{2} and 30\sqrt{2} to get 36\sqrt{2}.

$$36\sqrt{2}-4\sqrt{8}-\sqrt{50}$$

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}.

$$36\sqrt{2}-4\times 2\sqrt{2}-\sqrt{50}$$

Multiply -4 and 2 to get -8.

$$36\sqrt{2}-8\sqrt{2}-\sqrt{50}$$

Combine 36\sqrt{2} and -8\sqrt{2} to get 28\sqrt{2}.

$$28\sqrt{2}-\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$28\sqrt{2}-5\sqrt{2}$$

Combine 28\sqrt{2} and -5\sqrt{2} to get 23\sqrt{2}.

$$23\sqrt{2}$$