Solve 3.2/2+1.2/2*sqrt{1+7.87/23.7}

$$\frac{ 3.2 }{ 2 } + \frac{ 1.2 }{ 2 } \times \sqrt{ 1+ \frac{ 7.87 }{ 23.7 } }$$

Evaluate

$$\frac{\sqrt{7482090}}{3950}+1.6\approx 2.292491375$$

Short Solution Steps

Expand \frac{3.2}{2} by multiplying both numerator and the denominator by 10.

$$\frac{32}{20}+\frac{1.2}{2}\sqrt{1+\frac{7.87}{23.7}}$$

Reduce the fraction \frac{32}{20} to lowest terms by extracting and canceling out 4.

$$\frac{8}{5}+\frac{1.2}{2}\sqrt{1+\frac{7.87}{23.7}}$$

Expand \frac{1.2}{2} by multiplying both numerator and the denominator by 10.

$$\frac{8}{5}+\frac{12}{20}\sqrt{1+\frac{7.87}{23.7}}$$

Reduce the fraction \frac{12}{20} to lowest terms by extracting and canceling out 4.

$$\frac{8}{5}+\frac{3}{5}\sqrt{1+\frac{7.87}{23.7}}$$

Expand \frac{7.87}{23.7} by multiplying both numerator and the denominator by 100.

$$\frac{8}{5}+\frac{3}{5}\sqrt{1+\frac{787}{2370}}$$

Convert 1 to fraction \frac{2370}{2370}.

$$\frac{8}{5}+\frac{3}{5}\sqrt{\frac{2370}{2370}+\frac{787}{2370}}$$

Since \frac{2370}{2370} and \frac{787}{2370} have the same denominator, add them by adding their numerators.

$$\frac{8}{5}+\frac{3}{5}\sqrt{\frac{2370+787}{2370}}$$

Add 2370 and 787 to get 3157.

$$\frac{8}{5}+\frac{3}{5}\sqrt{\frac{3157}{2370}}$$

Rewrite the square root of the division \sqrt{\frac{3157}{2370}} as the division of square roots \frac{\sqrt{3157}}{\sqrt{2370}}.

$$\frac{8}{5}+\frac{3}{5}\times \frac{\sqrt{3157}}{\sqrt{2370}}$$

Rationalize the denominator of \frac{\sqrt{3157}}{\sqrt{2370}} by multiplying numerator and denominator by \sqrt{2370}.

$$\frac{8}{5}+\frac{3}{5}\times \frac{\sqrt{3157}\sqrt{2370}}{\left(\sqrt{2370}\right)^{2}}$$

The square of \sqrt{2370} is 2370.

$$\frac{8}{5}+\frac{3}{5}\times \frac{\sqrt{3157}\sqrt{2370}}{2370}$$

To multiply \sqrt{3157} and \sqrt{2370}, multiply the numbers under the square root.

$$\frac{8}{5}+\frac{3}{5}\times \frac{\sqrt{7482090}}{2370}$$

Multiply \frac{3}{5} times \frac{\sqrt{7482090}}{2370} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{5}+\frac{3\sqrt{7482090}}{5\times 2370}$$

Cancel out 3 in both numerator and denominator.

$$\frac{8}{5}+\frac{\sqrt{7482090}}{5\times 790}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 5\times 790 is 5\times 790. Multiply \frac{8}{5} times \frac{790}{790}.

$$\frac{8\times 790}{5\times 790}+\frac{\sqrt{7482090}}{5\times 790}$$

Since \frac{8\times 790}{5\times 790} and \frac{\sqrt{7482090}}{5\times 790} have the same denominator, add them by adding their numerators.

$$\frac{8\times 790+\sqrt{7482090}}{5\times 790}$$

Do the multiplications in 8\times 790+\sqrt{7482090}.

$$\frac{6320+\sqrt{7482090}}{5\times 790}$$

Expand 5\times 790.

$$\frac{6320+\sqrt{7482090}}{3950}$$