Solve 2sqrt{3}+6sqrt{20}-7sqrt{45})*sqrt{5}-sqrt{60}

$$2 \sqrt { 3 } + 6 \sqrt { 20 } - 7 \sqrt { 45 } ) \cdot \sqrt { 5 } - \sqrt { 60 }$$

Evaluate

$$2\sqrt{3}-9\sqrt{5}\approx -16.660510182$$

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}.

$$2\sqrt{3}+6\times 2\sqrt{5}-7\sqrt{45}$$

Multiply 6 and 2 to get 12.

$$2\sqrt{3}+12\sqrt{5}-7\sqrt{45}$$

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}.

$$2\sqrt{3}+12\sqrt{5}-7\times 3\sqrt{5}$$

Multiply -7 and 3 to get -21.

$$2\sqrt{3}+12\sqrt{5}-21\sqrt{5}$$

Combine 12\sqrt{5} and -21\sqrt{5} to get -9\sqrt{5}.

$$2\sqrt{3}-9\sqrt{5}$$