Solve (sqrt{12}-2)*sqrt{3}+sqrt{18}*sqrt{2}-1/5sqrt{75}=

$$( \sqrt { 12 } - 2 ) \cdot \sqrt { 3 } + \sqrt { 18 } \cdot \sqrt { 2 } - \frac { 1 } { 5 } \sqrt { 75 } =$$

Evaluate

$$12-3\sqrt{3}\approx 6.803847577$$

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}.

$$\left(2\sqrt{3}-2\right)\sqrt{3}+\sqrt{18}\sqrt{2}-\frac{1}{5}\sqrt{75}$$

Use the distributive property to multiply 2\sqrt{3}-2 by \sqrt{3}.

$$2\left(\sqrt{3}\right)^{2}-2\sqrt{3}+\sqrt{18}\sqrt{2}-\frac{1}{5}\sqrt{75}$$

The square of \sqrt{3} is 3.

$$2\times 3-2\sqrt{3}+\sqrt{18}\sqrt{2}-\frac{1}{5}\sqrt{75}$$

Multiply 2 and 3 to get 6.

$$6-2\sqrt{3}+\sqrt{18}\sqrt{2}-\frac{1}{5}\sqrt{75}$$

Factor 18=2\times 9. Rewrite the square root of the product \sqrt{2\times 9} as the product of square roots \sqrt{2}\sqrt{9}.

$$6-2\sqrt{3}+\sqrt{2}\sqrt{9}\sqrt{2}-\frac{1}{5}\sqrt{75}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$6-2\sqrt{3}+2\sqrt{9}-\frac{1}{5}\sqrt{75}$$

Calculate the square root of 9 and get 3.

$$6-2\sqrt{3}+2\times 3-\frac{1}{5}\sqrt{75}$$

Multiply 2 and 3 to get 6.

$$6-2\sqrt{3}+6-\frac{1}{5}\sqrt{75}$$

Add 6 and 6 to get 12.

$$12-2\sqrt{3}-\frac{1}{5}\sqrt{75}$$

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}.

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

Cancel out 5 and 5.

$$12-2\sqrt{3}-\sqrt{3}$$

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

$$12-3\sqrt{3}$$

Factor

$$3 {(4 - \sqrt{3})} = 6.803847577$$