Solve 1/6sqrt{5}+3sqrt{20}-2sqrt{45}

$$1 / 6 \sqrt { 5 } + 3 \sqrt { 20 } - 2 \sqrt { 45 }$$

Evaluate

$$\frac{\sqrt{5}}{6}\approx 0.372677996$$

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}.

$$\frac{1}{6}\sqrt{5}+3\times 2\sqrt{5}-2\sqrt{45}$$

Multiply 3 and 2 to get 6.

$$\frac{1}{6}\sqrt{5}+6\sqrt{5}-2\sqrt{45}$$

Combine \frac{1}{6}\sqrt{5} and 6\sqrt{5} to get \frac{37}{6}\sqrt{5}.

$$\frac{37}{6}\sqrt{5}-2\sqrt{45}$$

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}.

$$\frac{37}{6}\sqrt{5}-2\times 3\sqrt{5}$$

Multiply -2 and 3 to get -6.

$$\frac{37}{6}\sqrt{5}-6\sqrt{5}$$

Combine \frac{37}{6}\sqrt{5} and -6\sqrt{5} to get \frac{1}{6}\sqrt{5}.

$$\frac{1}{6}\sqrt{5}$$