Solve 2.5sqrt{12}+2/3sqrt{27}-0.8sqrt{75}

$$2.5 \sqrt{ 12 } + \frac{ 2 }{ 3 } \sqrt{ 27 } -0.8 \sqrt{ 75 }$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2.5\times 2\sqrt{3}+\frac{2}{3}\sqrt{27}-0.8\sqrt{75}$$

Multiply 2.5 and 2 to get 5.

$$5\sqrt{3}+\frac{2}{3}\sqrt{27}-0.8\sqrt{75}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$5\sqrt{3}+\frac{2}{3}\times 3\sqrt{3}-0.8\sqrt{75}$$

Cancel out 3 and 3.

$$5\sqrt{3}+2\sqrt{3}-0.8\sqrt{75}$$

Combine 5\sqrt{3} and 2\sqrt{3} to get 7\sqrt{3}.

$$7\sqrt{3}-0.8\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$7\sqrt{3}-0.8\times 5\sqrt{3}$$

Multiply -0.8 and 5 to get -4.

$$7\sqrt{3}-4\sqrt{3}$$

Combine 7\sqrt{3} and -4\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}$$