Solve sqrt{32}-sqrt{75}-sqrt{05}-2sqrt{1/3}=

$$\sqrt { 32 } - \sqrt { 75 } - \sqrt { 05 } - 2 \sqrt { \frac { 1 } { 3 } } =$$

Evaluate

$$-\frac{17\sqrt{3}}{3}+4\sqrt{2}\approx -4.158100327$$

Short Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\sqrt{2}-\sqrt{75}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

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}.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0\times 5}-2\sqrt{\frac{1}{3}}$$

Multiply 0 and 5 to get 0.

$$4\sqrt{2}-5\sqrt{3}-\sqrt{0}-2\sqrt{\frac{1}{3}}$$

Calculate the square root of 0 and get 0.

$$4\sqrt{2}-5\sqrt{3}-0-2\sqrt{\frac{1}{3}}$$

Multiply -1 and 0 to get 0.

$$4\sqrt{2}-5\sqrt{3}+0-2\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$4\sqrt{2}-5\sqrt{3}+0-2\times \frac{\sqrt{3}}{3}$$

Express -2\times \frac{\sqrt{3}}{3} as a single fraction.

$$4\sqrt{2}-5\sqrt{3}+0+\frac{-2\sqrt{3}}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4\sqrt{2}-5\sqrt{3}+0 times \frac{3}{3}.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3}+\frac{-2\sqrt{3}}{3}$$

Since \frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)}{3} and \frac{-2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

$$\frac{3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3}}{3}$$

Do the multiplications in 3\left(4\sqrt{2}-5\sqrt{3}+0\right)-2\sqrt{3}.

$$\frac{12\sqrt{2}-15\sqrt{3}-2\sqrt{3}}{3}$$

Do the calculations in 12\sqrt{2}-15\sqrt{3}-2\sqrt{3}.

$$\frac{12\sqrt{2}-17\sqrt{3}}{3}$$