Solve sqrt{153*0.18/0.68*0.32}

$$\sqrt { \frac { 153 \times 0.18 } { 0.68 \times 0.32 } }$$

Evaluate

$$11.25$$

Solution Steps

Multiply 153 and 0.18 to get 27.54.

$$\sqrt{\frac{27.54}{0.68\times 0.32}}$$

Multiply 0.68 and 0.32 to get 0.2176.

$$\sqrt{\frac{27.54}{0.2176}}$$

Expand \frac{27.54}{0.2176} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{275400}{2176}}$$

Reduce the fraction \frac{275400}{2176} to lowest terms by extracting and canceling out 136.

$$\sqrt{\frac{2025}{16}}$$

Rewrite the square root of the division \frac{2025}{16} as the division of square roots \frac{\sqrt{2025}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{45}{4}$$

Factor

$$\frac{5 \cdot 3 ^ {2}}{2 ^ {2}} = 11\frac{1}{4} = 11.25$$