Solve 1/16(1+4*5/8+sqrt{1+24*5/8})

$$\frac { 1 } { 16 } ( 1 + 4 \times \frac { 5 } { 8 } + \sqrt { 1 + 24 \cdot \frac { 5 } { 8 } } )$$

Evaluate

$$\frac{15}{32}=0.46875$$

Solution Steps

Express 4\times \frac{5}{8} as a single fraction.

$$\frac{1}{16}\left(1+\frac{4\times 5}{8}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Multiply 4 and 5 to get 20.

$$\frac{1}{16}\left(1+\frac{20}{8}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{1}{16}\left(1+\frac{5}{2}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{16}\left(\frac{2}{2}+\frac{5}{2}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Since \frac{2}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{16}\left(\frac{2+5}{2}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Add 2 and 5 to get 7.

$$\frac{1}{16}\left(\frac{7}{2}+\sqrt{1+24\times \frac{5}{8}}\right)$$

Express 24\times \frac{5}{8} as a single fraction.

$$\frac{1}{16}\left(\frac{7}{2}+\sqrt{1+\frac{24\times 5}{8}}\right)$$

Multiply 24 and 5 to get 120.

$$\frac{1}{16}\left(\frac{7}{2}+\sqrt{1+\frac{120}{8}}\right)$$

Divide 120 by 8 to get 15.

$$\frac{1}{16}\left(\frac{7}{2}+\sqrt{1+15}\right)$$

Add 1 and 15 to get 16.

$$\frac{1}{16}\left(\frac{7}{2}+\sqrt{16}\right)$$

Calculate the square root of 16 and get 4.

$$\frac{1}{16}\left(\frac{7}{2}+4\right)$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{1}{16}\left(\frac{7}{2}+\frac{8}{2}\right)$$

Since \frac{7}{2} and \frac{8}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{16}\times \frac{7+8}{2}$$

Add 7 and 8 to get 15.

$$\frac{1}{16}\times \frac{15}{2}$$

Multiply \frac{1}{16} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 15}{16\times 2}$$

Do the multiplications in the fraction \frac{1\times 15}{16\times 2}.

$$\frac{15}{32}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {5}} = 0.46875$$