Solve sqrt{2}-sqrt{40}+3sqrt{50}-9sqrt{90}

$$\sqrt { 2 } - \sqrt { 40 } + 3 \sqrt { 50 } - 9 \sqrt { 90 }$$

Evaluate

$$16\sqrt{2}-29\sqrt{10}\approx -69.078635147$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\sqrt{2}-2\sqrt{10}+3\sqrt{50}-9\sqrt{90}$$

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}.

$$\sqrt{2}-2\sqrt{10}+3\times 5\sqrt{2}-9\sqrt{90}$$

Multiply 3 and 5 to get 15.

$$\sqrt{2}-2\sqrt{10}+15\sqrt{2}-9\sqrt{90}$$

Combine \sqrt{2} and 15\sqrt{2} to get 16\sqrt{2}.

$$16\sqrt{2}-2\sqrt{10}-9\sqrt{90}$$

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$16\sqrt{2}-2\sqrt{10}-9\times 3\sqrt{10}$$

Multiply -9 and 3 to get -27.

$$16\sqrt{2}-2\sqrt{10}-27\sqrt{10}$$

Combine -2\sqrt{10} and -27\sqrt{10} to get -29\sqrt{10}.

$$16\sqrt{2}-29\sqrt{10}$$