Solve sqrt{((589div0.67}

$$\sqrt{ ((589 \div 0.67 }$$

Evaluate

$$\frac{10\sqrt{39463}}{67}\approx 29.64969608$$

Solution Steps

Expand \frac{589}{0.67} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{58900}{67}}$$

Rewrite the square root of the division \sqrt{\frac{58900}{67}} as the division of square roots \frac{\sqrt{58900}}{\sqrt{67}}.

$$\frac{\sqrt{58900}}{\sqrt{67}}$$

Factor 58900=10^{2}\times 589. Rewrite the square root of the product \sqrt{10^{2}\times 589} as the product of square roots \sqrt{10^{2}}\sqrt{589}. Take the square root of 10^{2}.

$$\frac{10\sqrt{589}}{\sqrt{67}}$$

Rationalize the denominator of \frac{10\sqrt{589}}{\sqrt{67}} by multiplying numerator and denominator by \sqrt{67}.

$$\frac{10\sqrt{589}\sqrt{67}}{\left(\sqrt{67}\right)^{2}}$$

The square of \sqrt{67} is 67.

$$\frac{10\sqrt{589}\sqrt{67}}{67}$$

To multiply \sqrt{589} and \sqrt{67}, multiply the numbers under the square root.

$$\frac{10\sqrt{39463}}{67}$$