Solve 1/3sqrt{3}-sqrt{32}+2sqrt{20}

$$\frac { 1 } { 3 } \sqrt { 3 } - \sqrt { 32 } + 2 \sqrt { 20 }$$

Evaluate

$$\frac{\sqrt{3}}{3}+4\sqrt{5}-4\sqrt{2}\approx 3.86476793$$

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}.

$$\frac{1}{3}\sqrt{3}-4\sqrt{2}+2\sqrt{20}$$

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}.

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

Multiply 2 and 2 to get 4.

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

Factor

$$\frac{\sqrt{3} + 12 \sqrt{5} - 12 \sqrt{2}}{3} = 3.8647679296964044$$