Solve 2sqrt{20}-sqrt{20/3}

$$2 \sqrt{ 20 } - \sqrt{ \frac{ 20 }{ 3 } }$$

Evaluate

$$-\frac{2\sqrt{15}}{3}+4\sqrt{5}\approx 6.362283013$$

Short Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$2\times 2\sqrt{5}-\sqrt{\frac{20}{3}}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{5}-\sqrt{\frac{20}{3}}$$

Rewrite the square root of the division \sqrt{\frac{20}{3}} as the division of square roots \frac{\sqrt{20}}{\sqrt{3}}.

$$4\sqrt{5}-\frac{\sqrt{20}}{\sqrt{3}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

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

Rationalize the denominator of \frac{2\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$4\sqrt{5}-\frac{2\sqrt{15}}{3}$$

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

$$\frac{3\times 4\sqrt{5}}{3}-\frac{2\sqrt{15}}{3}$$

Since \frac{3\times 4\sqrt{5}}{3} and \frac{2\sqrt{15}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 4\sqrt{5}-2\sqrt{15}}{3}$$

Do the multiplications in 3\times 4\sqrt{5}-2\sqrt{15}.

$$\frac{12\sqrt{5}-2\sqrt{15}}{3}$$