Solve frac{2sqrt{12}+2sqrt{8}}{12*18}

$$\frac { 2 \sqrt { 12 } + 2 \sqrt { 8 } } { 12 \times 18 }$$

Evaluate

$$\frac{\sqrt{2}+\sqrt{3}}{54}\approx 0.058264155$$

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}.

$$\frac{2\times 2\sqrt{3}+2\sqrt{8}}{12\times 18}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}+2\sqrt{8}}{12\times 18}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{4\sqrt{3}+2\times 2\sqrt{2}}{12\times 18}$$

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{3}+4\sqrt{2}}{12\times 18}$$

Multiply 12 and 18 to get 216.

$$\frac{4\sqrt{3}+4\sqrt{2}}{216}$$

Factor

$$\frac{\sqrt{2} + \sqrt{3}}{54} = 0.05826415499892542$$