Solve 210/24/frac{24{10*sqrt{20}}}=

$$\frac { 2 \frac { 10 } { 24 } } { \frac { 24 } { 10 \cdot \sqrt { 20 } } } =$$

Evaluate

$$\frac{145\sqrt{5}}{72}\approx 4.503192455$$

Solution Steps

Divide \frac{2\times 24+10}{24} by \frac{24}{10\sqrt{20}} by multiplying \frac{2\times 24+10}{24} by the reciprocal of \frac{24}{10\sqrt{20}}.

$$\frac{\left(2\times 24+10\right)\times 10\sqrt{20}}{24\times 24}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{20}\left(10+2\times 24\right)}{12\times 24}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{5\times 2\sqrt{5}\left(10+2\times 24\right)}{12\times 24}$$

Multiply 5 and 2 to get 10.

$$\frac{10\sqrt{5}\left(10+2\times 24\right)}{12\times 24}$$

Multiply 2 and 24 to get 48.

$$\frac{10\sqrt{5}\left(10+48\right)}{12\times 24}$$

Add 10 and 48 to get 58.

$$\frac{10\sqrt{5}\times 58}{12\times 24}$$

Multiply 10 and 58 to get 580.

$$\frac{580\sqrt{5}}{12\times 24}$$

Multiply 12 and 24 to get 288.

$$\frac{580\sqrt{5}}{288}$$

Divide 580\sqrt{5} by 288 to get \frac{145}{72}\sqrt{5}.

$$\frac{145}{72}\sqrt{5}$$