Solve sqrt{20}+sqrt{18}-5sqrt{8}+sqrt{98}2sqrt{45}

$$\sqrt { 20 } + \sqrt { 18 } - 5 \sqrt { 8 } + \sqrt { 98 } 2 \sqrt { 45 }$$

Evaluate

$$2\sqrt{5}+42\sqrt{10}-7\sqrt{2}\approx 127.388302745$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\sqrt{5}+\sqrt{18}-5\sqrt{8}+2\sqrt{98}\sqrt{45}$$

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}.

$$2\sqrt{5}+3\sqrt{2}-5\sqrt{8}+2\sqrt{98}\sqrt{45}$$

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}.

$$2\sqrt{5}+3\sqrt{2}-5\times 2\sqrt{2}+2\sqrt{98}\sqrt{45}$$

Multiply -5 and 2 to get -10.

$$2\sqrt{5}+3\sqrt{2}-10\sqrt{2}+2\sqrt{98}\sqrt{45}$$

Combine 3\sqrt{2} and -10\sqrt{2} to get -7\sqrt{2}.

$$2\sqrt{5}-7\sqrt{2}+2\sqrt{98}\sqrt{45}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$2\sqrt{5}-7\sqrt{2}+2\times 7\sqrt{2}\sqrt{45}$$

Multiply 2 and 7 to get 14.

$$2\sqrt{5}-7\sqrt{2}+14\sqrt{2}\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$2\sqrt{5}-7\sqrt{2}+14\sqrt{2}\times 3\sqrt{5}$$

Multiply 14 and 3 to get 42.

$$2\sqrt{5}-7\sqrt{2}+42\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$2\sqrt{5}-7\sqrt{2}+42\sqrt{10}$$