Solve frac{sqrt{15}+sqrt{12}}{3}*(sqrt{5}-2)

$$\frac { \sqrt { 15 } + \sqrt { 12 } } { 3 } \cdot ( \sqrt { 5 } - 2 )$$

Evaluate

$$\frac{\sqrt{3}}{3}\approx 0.577350269$$

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}.

$$\frac{\sqrt{15}+2\sqrt{3}}{3}\left(\sqrt{5}-2\right)$$

Express \frac{\sqrt{15}+2\sqrt{3}}{3}\left(\sqrt{5}-2\right) as a single fraction.

$$\frac{\left(\sqrt{15}+2\sqrt{3}\right)\left(\sqrt{5}-2\right)}{3}$$

Apply the distributive property by multiplying each term of \sqrt{15}+2\sqrt{3} by each term of \sqrt{5}-2.

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

Factor 15=5\times 3. Rewrite the square root of the product \sqrt{5\times 3} as the product of square roots \sqrt{5}\sqrt{3}.

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

Multiply \sqrt{5} and \sqrt{5} to get 5.

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

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

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

Combine -2\sqrt{15} and 2\sqrt{15} to get 0.

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

Combine 5\sqrt{3} and -4\sqrt{3} to get \sqrt{3}.

$$\frac{\sqrt{3}}{3}$$