Solve 2sqrt{80}-sqrt{45}+2sqrt{63}

$$2 \sqrt{ 80 } - \sqrt{ 45 } +2 \sqrt{ 63 }$$

Evaluate

$$5\sqrt{5}+6\sqrt{7}\approx 27.054847754$$

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}.

$$2\times 4\sqrt{5}-\sqrt{45}+2\sqrt{63}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{5}-\sqrt{45}+2\sqrt{63}$$

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}.

$$8\sqrt{5}-3\sqrt{5}+2\sqrt{63}$$

Combine 8\sqrt{5} and -3\sqrt{5} to get 5\sqrt{5}.

$$5\sqrt{5}+2\sqrt{63}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

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

Multiply 2 and 3 to get 6.

$$5\sqrt{5}+6\sqrt{7}$$