Solve 3sqrt{2}+sqrt{90}+2sqrt{160}-sqrt{18}

$$3 \sqrt{ 2 } + \sqrt{ 90 } +2 \sqrt{ 160 } - \sqrt{ 18 }$$

Evaluate

$$11\sqrt{10}\approx 34.785054262$$

Solution Steps

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}.

$$3\sqrt{2}+3\sqrt{10}+2\sqrt{160}-\sqrt{18}$$

Factor 160=4^{2}\times 10. Rewrite the square root of the product \sqrt{4^{2}\times 10} as the product of square roots \sqrt{4^{2}}\sqrt{10}. Take the square root of 4^{2}.

$$3\sqrt{2}+3\sqrt{10}+2\times 4\sqrt{10}-\sqrt{18}$$

Multiply 2 and 4 to get 8.

$$3\sqrt{2}+3\sqrt{10}+8\sqrt{10}-\sqrt{18}$$

Combine 3\sqrt{10} and 8\sqrt{10} to get 11\sqrt{10}.

$$3\sqrt{2}+11\sqrt{10}-\sqrt{18}$$

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}.

$$3\sqrt{2}+11\sqrt{10}-3\sqrt{2}$$

Combine 3\sqrt{2} and -3\sqrt{2} to get 0.

$$11\sqrt{10}$$