Solve sqrt{6^2-19*7div5}

$$\sqrt { 6 ^ { 2 } - 19 \times 7 \div 5 }$$

Evaluate

$$\frac{\sqrt{235}}{5}\approx 3.065941943$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$\sqrt{36-\frac{19\times 7}{5}}$$

Multiply 19 and 7 to get 133.

$$\sqrt{36-\frac{133}{5}}$$

Convert 36 to fraction \frac{180}{5}.

$$\sqrt{\frac{180}{5}-\frac{133}{5}}$$

Since \frac{180}{5} and \frac{133}{5} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{180-133}{5}}$$

Subtract 133 from 180 to get 47.

$$\sqrt{\frac{47}{5}}$$

Rewrite the square root of the division \sqrt{\frac{47}{5}} as the division of square roots \frac{\sqrt{47}}{\sqrt{5}}.

$$\frac{\sqrt{47}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{47}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{47}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{47}\sqrt{5}}{5}$$

To multiply \sqrt{47} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{235}}{5}$$