Solve 0.5sqrt{12}-3sqrt{27}+0.4sqrt{75}

$$0.5 \sqrt{ 12 } -3 \sqrt{ 27 } +0.4 \sqrt{ 75 }$$

Evaluate

$$-6\sqrt{3}\approx -10.392304845$$

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}.

$$0.5\times 2\sqrt{3}-3\sqrt{27}+0.4\sqrt{75}$$

Multiply 0.5 and 2 to get 1.

$$\sqrt{3}-3\sqrt{27}+0.4\sqrt{75}$$

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}.

$$\sqrt{3}-3\times 3\sqrt{3}+0.4\sqrt{75}$$

Multiply -3 and 3 to get -9.

$$\sqrt{3}-9\sqrt{3}+0.4\sqrt{75}$$

Combine \sqrt{3} and -9\sqrt{3} to get -8\sqrt{3}.

$$-8\sqrt{3}+0.4\sqrt{75}$$

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}.

$$-8\sqrt{3}+0.4\times 5\sqrt{3}$$

Multiply 0.4 and 5 to get 2.

$$-8\sqrt{3}+2\sqrt{3}$$

Combine -8\sqrt{3} and 2\sqrt{3} to get -6\sqrt{3}.

$$-6\sqrt{3}$$