Solve 0,6sqrt{75}-2/3sqrt{27}+1,5sqrt{12}

$$0,6 \sqrt { 75 } - \frac { 2 } { 3 } \sqrt { 27 } + 1,5 \sqrt { 12 }$$

Evaluate

$$4\sqrt{3}\approx 6.92820323$$

Solution Steps

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}.

$$0,6\times 5\sqrt{3}-\frac{2}{3}\sqrt{27}+1,5\sqrt{12}$$

Multiply 0,6 and 5 to get 3.

$$3\sqrt{3}-\frac{2}{3}\sqrt{27}+1,5\sqrt{12}$$

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}.

$$3\sqrt{3}-\frac{2}{3}\times 3\sqrt{3}+1,5\sqrt{12}$$

Cancel out 3 and 3.

$$3\sqrt{3}-2\sqrt{3}+1,5\sqrt{12}$$

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

$$\sqrt{3}+1,5\sqrt{12}$$

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}.

$$\sqrt{3}+1,5\times 2\sqrt{3}$$

Multiply 1,5 and 2 to get 3.

$$\sqrt{3}+3\sqrt{3}$$

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

$$4\sqrt{3}$$