Solve 209frac{sqrt{336}}{113/4}

$$209 \frac { \sqrt { 336 } } { 11 \frac { 3 } { 4 } }$$

Evaluate

$$\frac{3344\sqrt{21}}{47}\approx 326.045385616$$

Solution Steps

Factor 336=4^{2}\times 21. Rewrite the square root of the product \sqrt{4^{2}\times 21} as the product of square roots \sqrt{4^{2}}\sqrt{21}. Take the square root of 4^{2}.

$$209\times \frac{4\sqrt{21}}{\frac{11\times 4+3}{4}}$$

Multiply 11 and 4 to get 44.

$$209\times \frac{4\sqrt{21}}{\frac{44+3}{4}}$$

Add 44 and 3 to get 47.

$$209\times \frac{4\sqrt{21}}{\frac{47}{4}}$$

Divide 4\sqrt{21} by \frac{47}{4} by multiplying 4\sqrt{21} by the reciprocal of \frac{47}{4}.

$$209\times \frac{4\sqrt{21}\times 4}{47}$$

Multiply 4 and 4 to get 16.

$$209\times \frac{16\sqrt{21}}{47}$$

Express 209\times \frac{16\sqrt{21}}{47} as a single fraction.

$$\frac{209\times 16\sqrt{21}}{47}$$

Multiply 209 and 16 to get 3344.

$$\frac{3344\sqrt{21}}{47}$$