Solve frac{sqrt{32}}{sqrt{75}*sqrt{48}}

$$\frac { \sqrt { 32 } } { \sqrt { 75 } \times \sqrt { 48 } }$$

Evaluate

$$\frac{\sqrt{2}}{15}\approx 0.094280904$$

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}.

$$\frac{4\sqrt{2}}{\sqrt{75}\sqrt{48}}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{4\sqrt{2}}{5\sqrt{3}\sqrt{48}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Multiply 5 and 4 to get 20.

$$\frac{4\sqrt{2}}{20\sqrt{3}\sqrt{3}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{4\sqrt{2}}{20\times 3}$$

Multiply 20 and 3 to get 60.

$$\frac{4\sqrt{2}}{60}$$

Divide 4\sqrt{2} by 60 to get \frac{1}{15}\sqrt{2}.

$$\frac{1}{15}\sqrt{2}$$