Solve 5div5*6-5+3sqrt{5%7}

$$5 \div 5 \times 6-5+3 \sqrt{ 5 \% 7 }$$

Evaluate

$$\frac{3\sqrt{35}}{10}+1\approx 2.774823935$$

Short Solution Steps

Divide 5 by 5 to get 1.

$$1\times 6-5+3\sqrt{\frac{5}{100}\times 7}$$

Multiply 1 and 6 to get 6.

$$6-5+3\sqrt{\frac{5}{100}\times 7}$$

Subtract 5 from 6 to get 1.

$$1+3\sqrt{\frac{5}{100}\times 7}$$

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$1+3\sqrt{\frac{1}{20}\times 7}$$

Multiply \frac{1}{20} and 7 to get \frac{7}{20}.

$$1+3\sqrt{\frac{7}{20}}$$

Rewrite the square root of the division \sqrt{\frac{7}{20}} as the division of square roots \frac{\sqrt{7}}{\sqrt{20}}.

$$1+3\times \frac{\sqrt{7}}{\sqrt{20}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$1+3\times \frac{\sqrt{7}}{2\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{7}}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$1+3\times \frac{\sqrt{7}\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$1+3\times \frac{\sqrt{7}\sqrt{5}}{2\times 5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$1+3\times \frac{\sqrt{35}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$1+3\times \frac{\sqrt{35}}{10}$$

Express 3\times \frac{\sqrt{35}}{10} as a single fraction.

$$1+\frac{3\sqrt{35}}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{10}{10}.

$$\frac{10}{10}+\frac{3\sqrt{35}}{10}$$

Since \frac{10}{10} and \frac{3\sqrt{35}}{10} have the same denominator, add them by adding their numerators.

$$\frac{10+3\sqrt{35}}{10}$$