Solve sqrt{39+598div5}-52

$$\sqrt{ 39+598 \div 5 } -52$$

Evaluate

$$\frac{\sqrt{3965}}{5}-52\approx -39.406350807$$

Short Solution Steps

Convert 39 to fraction \frac{195}{5}.

$$\sqrt{\frac{195}{5}+\frac{598}{5}}-52$$

Since \frac{195}{5} and \frac{598}{5} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{195+598}{5}}-52$$

Add 195 and 598 to get 793.

$$\sqrt{\frac{793}{5}}-52$$

Rewrite the square root of the division \sqrt{\frac{793}{5}} as the division of square roots \frac{\sqrt{793}}{\sqrt{5}}.

$$\frac{\sqrt{793}}{\sqrt{5}}-52$$

Rationalize the denominator of \frac{\sqrt{793}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{793}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}-52$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{793}\sqrt{5}}{5}-52$$

To multiply \sqrt{793} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{3965}}{5}-52$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 52 times \frac{5}{5}.

$$\frac{\sqrt{3965}}{5}-\frac{52\times 5}{5}$$

Since \frac{\sqrt{3965}}{5} and \frac{52\times 5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{3965}-52\times 5}{5}$$

Do the multiplications in \sqrt{3965}-52\times 5.

$$\frac{\sqrt{3965}-260}{5}$$