Solve 8+17-1/sqrt{16+16+4*sqrt{4+17/16+1/4}}=

$$\frac { 8 + 17 - 1 } { \sqrt { 16 + 16 + 4 } \cdot \sqrt { 4 + \frac { 17 } { 16 } + \frac { 1 } { 4 } } } =$$

Evaluate

$$\frac{16\sqrt{85}}{85}\approx 1.735443663$$

Solution Steps

Add 8 and 17 to get 25.

$$\frac{25-1}{\sqrt{16+16+4}\sqrt{4+\frac{17}{16}+\frac{1}{4}}}$$

Subtract 1 from 25 to get 24.

$$\frac{24}{\sqrt{16+16+4}\sqrt{4+\frac{17}{16}+\frac{1}{4}}}$$

Add 16 and 16 to get 32.

$$\frac{24}{\sqrt{32+4}\sqrt{4+\frac{17}{16}+\frac{1}{4}}}$$

Add 32 and 4 to get 36.

$$\frac{24}{\sqrt{36}\sqrt{4+\frac{17}{16}+\frac{1}{4}}}$$

Calculate the square root of 36 and get 6.

$$\frac{24}{6\sqrt{4+\frac{17}{16}+\frac{1}{4}}}$$

Convert 4 to fraction \frac{64}{16}.

$$\frac{24}{6\sqrt{\frac{64}{16}+\frac{17}{16}+\frac{1}{4}}}$$

Since \frac{64}{16} and \frac{17}{16} have the same denominator, add them by adding their numerators.

$$\frac{24}{6\sqrt{\frac{64+17}{16}+\frac{1}{4}}}$$

Add 64 and 17 to get 81.

$$\frac{24}{6\sqrt{\frac{81}{16}+\frac{1}{4}}}$$

Least common multiple of 16 and 4 is 16. Convert \frac{81}{16} and \frac{1}{4} to fractions with denominator 16.

$$\frac{24}{6\sqrt{\frac{81}{16}+\frac{4}{16}}}$$

Since \frac{81}{16} and \frac{4}{16} have the same denominator, add them by adding their numerators.

$$\frac{24}{6\sqrt{\frac{81+4}{16}}}$$

Add 81 and 4 to get 85.

$$\frac{24}{6\sqrt{\frac{85}{16}}}$$

Rewrite the square root of the division \sqrt{\frac{85}{16}} as the division of square roots \frac{\sqrt{85}}{\sqrt{16}}.

$$\frac{24}{6\times \frac{\sqrt{85}}{\sqrt{16}}}$$

Calculate the square root of 16 and get 4.

$$\frac{24}{6\times \frac{\sqrt{85}}{4}}$$

Express 6\times \frac{\sqrt{85}}{4} as a single fraction.

$$\frac{24}{\frac{6\sqrt{85}}{4}}$$

Divide 24 by \frac{6\sqrt{85}}{4} by multiplying 24 by the reciprocal of \frac{6\sqrt{85}}{4}.

$$\frac{24\times 4}{6\sqrt{85}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{4\times 4}{\sqrt{85}}$$

Rationalize the denominator of \frac{4\times 4}{\sqrt{85}} by multiplying numerator and denominator by \sqrt{85}.

$$\frac{4\times 4\sqrt{85}}{\left(\sqrt{85}\right)^{2}}$$

The square of \sqrt{85} is 85.

$$\frac{4\times 4\sqrt{85}}{85}$$

Multiply 4 and 4 to get 16.

$$\frac{16\sqrt{85}}{85}$$