Solve frac{frac{sqrt{45*12}}{12}}{8}

$$\frac{ \frac{ \sqrt{ 45 \times 12 } }{ 12 } }{ 8 }$$

Evaluate

$$\frac{\sqrt{15}}{16}\approx 0.242061459$$

Solution Steps

Express \frac{\frac{\sqrt{45\times 12}}{12}}{8} as a single fraction.

$$\frac{\sqrt{45\times 12}}{12\times 8}$$

Multiply 45 and 12 to get 540.

$$\frac{\sqrt{540}}{12\times 8}$$

Factor 540=6^{2}\times 15. Rewrite the square root of the product \sqrt{6^{2}\times 15} as the product of square roots \sqrt{6^{2}}\sqrt{15}. Take the square root of 6^{2}.

$$\frac{6\sqrt{15}}{12\times 8}$$

Multiply 12 and 8 to get 96.

$$\frac{6\sqrt{15}}{96}$$

Divide 6\sqrt{15} by 96 to get \frac{1}{16}\sqrt{15}.

$$\frac{1}{16}\sqrt{15}$$