Solve 3sqrt{54}-2sqrt{45}-sqrt{45}

$$3 \sqrt { 54 } - 2 \sqrt { 45 } - \sqrt { 45 }$$

Evaluate

$$9\left(\sqrt{6}-\sqrt{5}\right)\approx 1.920795888$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\times 3\sqrt{6}-2\sqrt{45}-\sqrt{45}$$

Multiply 3 and 3 to get 9.

$$9\sqrt{6}-2\sqrt{45}-\sqrt{45}$$

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}.

$$9\sqrt{6}-2\times 3\sqrt{5}-\sqrt{45}$$

Multiply -2 and 3 to get -6.

$$9\sqrt{6}-6\sqrt{5}-\sqrt{45}$$

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}.

$$9\sqrt{6}-6\sqrt{5}-3\sqrt{5}$$

Combine -6\sqrt{5} and -3\sqrt{5} to get -9\sqrt{5}.

$$9\sqrt{6}-9\sqrt{5}$$