Solve frac{3sqrt{24}}{20}+10/20

$$\frac { 3 \sqrt { 24 } } { 20 } + \frac { 10 } { 20 }$$

Evaluate

$$\frac{3\sqrt{6}}{10}+\frac{1}{2}\approx 1.234846923$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{6}}{20}+\frac{10}{20}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{6}}{20}+\frac{10}{20}$$

Divide 6\sqrt{6} by 20 to get \frac{3}{10}\sqrt{6}.

$$\frac{3}{10}\sqrt{6}+\frac{10}{20}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$\frac{3}{10}\sqrt{6}+\frac{1}{2}$$

Factor

$$\frac{3 \sqrt{6} + 5}{10} = 1.2348469228349532$$