Solve sqrt{8^2-3/frac{6{5}}+3*89}

$$\sqrt{ \frac{ { 8 }^{ 2 } -3 }{ \frac{ 6 }{ 5 } } +3 \times 89 }$$

Evaluate

$$\frac{\sqrt{11442}}{6}\approx 17.827880786$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{\frac{64-3}{\frac{6}{5}}+3\times 89}$$

Subtract 3 from 64 to get 61.

$$\sqrt{\frac{61}{\frac{6}{5}}+3\times 89}$$

Divide 61 by \frac{6}{5} by multiplying 61 by the reciprocal of \frac{6}{5}.

$$\sqrt{61\times \frac{5}{6}+3\times 89}$$

Express 61\times \frac{5}{6} as a single fraction.

$$\sqrt{\frac{61\times 5}{6}+3\times 89}$$

Multiply 61 and 5 to get 305.

$$\sqrt{\frac{305}{6}+3\times 89}$$

Multiply 3 and 89 to get 267.

$$\sqrt{\frac{305}{6}+267}$$

Convert 267 to fraction \frac{1602}{6}.

$$\sqrt{\frac{305}{6}+\frac{1602}{6}}$$

Since \frac{305}{6} and \frac{1602}{6} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{305+1602}{6}}$$

Add 305 and 1602 to get 1907.

$$\sqrt{\frac{1907}{6}}$$

Rewrite the square root of the division \sqrt{\frac{1907}{6}} as the division of square roots \frac{\sqrt{1907}}{\sqrt{6}}.

$$\frac{\sqrt{1907}}{\sqrt{6}}$$

Rationalize the denominator of \frac{\sqrt{1907}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{1907}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{1907}\sqrt{6}}{6}$$

To multiply \sqrt{1907} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{11442}}{6}$$