Solve 2sqrt{20}+2/3sqrt{45}-5/4sqrt{80}-sqrt{5}

$$2 \sqrt{ 20 } + \frac{ 2 }{ 3 } \sqrt{ 45 } - \frac{ 5 }{ 4 } \sqrt{ 80 } - \sqrt{ 5 }$$

Evaluate

$$0$$

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}.

$$2\times 2\sqrt{5}+\frac{2}{3}\sqrt{45}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}+\frac{2}{3}\sqrt{45}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

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}.

$$4\sqrt{5}+\frac{2}{3}\times 3\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Cancel out 3 and 3.

$$4\sqrt{5}+2\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

Combine 4\sqrt{5} and 2\sqrt{5} to get 6\sqrt{5}.

$$6\sqrt{5}-\frac{5}{4}\sqrt{80}-\sqrt{5}$$

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}.

$$6\sqrt{5}-\frac{5}{4}\times 4\sqrt{5}-\sqrt{5}$$

Cancel out 4 and 4.

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

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

$$\sqrt{5}-\sqrt{5}$$

Combine \sqrt{5} and -\sqrt{5} to get 0.

$$0$$

Factor

$$0$$