Solve 16*frac{9sqrt{17}}{36-75div4}

$$16 \times \frac{ 9 \sqrt{ 17 } }{ 36-75 \div 4 }$$

Evaluate

$$\frac{192\sqrt{17}}{23}\approx 34.418968701$$

Solution Steps

Convert 36 to fraction \frac{144}{4}.

$$16\times \frac{9\sqrt{17}}{\frac{144}{4}-\frac{75}{4}}$$

Since \frac{144}{4} and \frac{75}{4} have the same denominator, subtract them by subtracting their numerators.

$$16\times \frac{9\sqrt{17}}{\frac{144-75}{4}}$$

Subtract 75 from 144 to get 69.

$$16\times \frac{9\sqrt{17}}{\frac{69}{4}}$$

Divide 9\sqrt{17} by \frac{69}{4} by multiplying 9\sqrt{17} by the reciprocal of \frac{69}{4}.

$$16\times \frac{9\sqrt{17}\times 4}{69}$$

Multiply 9 and 4 to get 36.

$$16\times \frac{36\sqrt{17}}{69}$$

Divide 36\sqrt{17} by 69 to get \frac{12}{23}\sqrt{17}.

$$16\times \frac{12}{23}\sqrt{17}$$

Express 16\times \frac{12}{23} as a single fraction.

$$\frac{16\times 12}{23}\sqrt{17}$$

Multiply 16 and 12 to get 192.

$$\frac{192}{23}\sqrt{17}$$