Solve left(3sqrt{5}-sqrt{80}+4sqrt{20}right)sqrt{245}

$$\left( 3 \sqrt{ 5 } - \sqrt{ 80 } +4 \sqrt{ 20 } \right) \sqrt{ 245 }$$

Evaluate

$$245$$

Solution Steps

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\left(3\sqrt{5}-4\sqrt{5}+4\sqrt{20}\right)\sqrt{245}$$

Combine 3\sqrt{5} and -4\sqrt{5} to get -\sqrt{5}.

$$\left(-\sqrt{5}+4\sqrt{20}\right)\sqrt{245}$$

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}.

$$\left(-\sqrt{5}+4\times 2\sqrt{5}\right)\sqrt{245}$$

Multiply 4 and 2 to get 8.

$$\left(-\sqrt{5}+8\sqrt{5}\right)\sqrt{245}$$

Combine -\sqrt{5} and 8\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}\sqrt{245}$$

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}.

$$7\sqrt{5}\times 7\sqrt{5}$$

Multiply 7 and 7 to get 49.

$$49\sqrt{5}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$49\times 5$$

Multiply 49 and 5 to get 245.

$$245$$

Factor

$$5\times 7^{2}$$