Solve 2sqrt{180}-14sqrt{20}+10sqrt{45}-sqrt{245}

$$2 \sqrt{ 180 } -14 \sqrt{ 20 } +10 \sqrt{ 45 } - \sqrt{ 245 }$$

Evaluate

$$7\sqrt{5}\approx 15.652475842$$

Solution Steps

Factor 180=6^{2}\times 5. Rewrite the square root of the product \sqrt{6^{2}\times 5} as the product of square roots \sqrt{6^{2}}\sqrt{5}. Take the square root of 6^{2}.

$$2\times 6\sqrt{5}-14\sqrt{20}+10\sqrt{45}-\sqrt{245}$$

Multiply 2 and 6 to get 12.

$$12\sqrt{5}-14\sqrt{20}+10\sqrt{45}-\sqrt{245}$$

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}.

$$12\sqrt{5}-14\times 2\sqrt{5}+10\sqrt{45}-\sqrt{245}$$

Multiply -14 and 2 to get -28.

$$12\sqrt{5}-28\sqrt{5}+10\sqrt{45}-\sqrt{245}$$

Combine 12\sqrt{5} and -28\sqrt{5} to get -16\sqrt{5}.

$$-16\sqrt{5}+10\sqrt{45}-\sqrt{245}$$

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}.

$$-16\sqrt{5}+10\times 3\sqrt{5}-\sqrt{245}$$

Multiply 10 and 3 to get 30.

$$-16\sqrt{5}+30\sqrt{5}-\sqrt{245}$$

Combine -16\sqrt{5} and 30\sqrt{5} to get 14\sqrt{5}.

$$14\sqrt{5}-\sqrt{245}$$

Factor 245=7^{2}\times 5. Rewrite the square root of the product \sqrt{7^{2}\times 5} as the product of square roots \sqrt{7^{2}}\sqrt{5}. Take the square root of 7^{2}.

$$14\sqrt{5}-7\sqrt{5}$$

Combine 14\sqrt{5} and -7\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}$$