Solve 17+1/72+16sqrt{8}+2/3+1/4

$$17 + \frac { 1 } { 72 } + 16 \sqrt { 8 } + \frac { 2 } { 3 } + \frac { 1 } { 4 }$$

Evaluate

$$32\sqrt{2}+\frac{1291}{72}\approx 63.185389551$$

Solution Steps

Convert 17 to fraction \frac{1224}{72}.

$$\frac{1224}{72}+\frac{1}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

Since \frac{1224}{72} and \frac{1}{72} have the same denominator, add them by adding their numerators.

$$\frac{1224+1}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

Add 1224 and 1 to get 1225.

$$\frac{1225}{72}+16\sqrt{8}+\frac{2}{3}+\frac{1}{4}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{1225}{72}+16\times 2\sqrt{2}+\frac{2}{3}+\frac{1}{4}$$

Multiply 16 and 2 to get 32.

$$\frac{1225}{72}+32\sqrt{2}+\frac{2}{3}+\frac{1}{4}$$

Least common multiple of 72 and 3 is 72. Convert \frac{1225}{72} and \frac{2}{3} to fractions with denominator 72.

$$\frac{1225}{72}+32\sqrt{2}+\frac{48}{72}+\frac{1}{4}$$

Since \frac{1225}{72} and \frac{48}{72} have the same denominator, add them by adding their numerators.

$$\frac{1225+48}{72}+32\sqrt{2}+\frac{1}{4}$$

Add 1225 and 48 to get 1273.

$$\frac{1273}{72}+32\sqrt{2}+\frac{1}{4}$$

Least common multiple of 72 and 4 is 72. Convert \frac{1273}{72} and \frac{1}{4} to fractions with denominator 72.

$$\frac{1273}{72}+32\sqrt{2}+\frac{18}{72}$$

Since \frac{1273}{72} and \frac{18}{72} have the same denominator, add them by adding their numerators.

$$\frac{1273+18}{72}+32\sqrt{2}$$

Add 1273 and 18 to get 1291.

$$\frac{1291}{72}+32\sqrt{2}$$

Factor

$$\frac{2304 \sqrt{2} + 1291}{72} = 63.18538955149461$$