Solve sqrt{2*85000/9.56}

$$\sqrt{ \frac{ 2 \times 85000 }{ 9.56 } }$$

Evaluate

$$\frac{500\sqrt{4063}}{239}\approx 133.350765945$$

Solution Steps

Multiply 2 and 85000 to get 170000.

$$\sqrt{\frac{170000}{9.56}}$$

Expand \frac{170000}{9.56} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{17000000}{956}}$$

Reduce the fraction \frac{17000000}{956} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{4250000}{239}}$$

Rewrite the square root of the division \sqrt{\frac{4250000}{239}} as the division of square roots \frac{\sqrt{4250000}}{\sqrt{239}}.

$$\frac{\sqrt{4250000}}{\sqrt{239}}$$

Factor 4250000=500^{2}\times 17. Rewrite the square root of the product \sqrt{500^{2}\times 17} as the product of square roots \sqrt{500^{2}}\sqrt{17}. Take the square root of 500^{2}.

$$\frac{500\sqrt{17}}{\sqrt{239}}$$

Rationalize the denominator of \frac{500\sqrt{17}}{\sqrt{239}} by multiplying numerator and denominator by \sqrt{239}.

$$\frac{500\sqrt{17}\sqrt{239}}{\left(\sqrt{239}\right)^{2}}$$

The square of \sqrt{239} is 239.

$$\frac{500\sqrt{17}\sqrt{239}}{239}$$

To multiply \sqrt{17} and \sqrt{239}, multiply the numbers under the square root.

$$\frac{500\sqrt{4063}}{239}$$