Solve 10sqrt{3}(frac{10sqrt{221}+50}{49})

$$10 \sqrt { 3 } ( \frac { 10 \sqrt { 221 } + 50 } { 49 } )$$

Evaluate

$$\frac{100\sqrt{3}\left(\sqrt{221}+5\right)}{49}\approx 70.222531463$$

Solution Steps

Express 10\times \frac{10\sqrt{221}+50}{49} as a single fraction.

$$\frac{10\left(10\sqrt{221}+50\right)}{49}\sqrt{3}$$

Use the distributive property to multiply 10 by 10\sqrt{221}+50.

$$\frac{100\sqrt{221}+500}{49}\sqrt{3}$$

Express \frac{100\sqrt{221}+500}{49}\sqrt{3} as a single fraction.

$$\frac{\left(100\sqrt{221}+500\right)\sqrt{3}}{49}$$

Use the distributive property to multiply 100\sqrt{221}+500 by \sqrt{3}.

$$\frac{100\sqrt{221}\sqrt{3}+500\sqrt{3}}{49}$$

To multiply \sqrt{221} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{100\sqrt{663}+500\sqrt{3}}{49}$$

Factor

$$\frac{100 \sqrt{3} {(\sqrt{221} + 5)}}{49} = 70.2225314632895$$