Solve sqrt{2*71.6/9.8}

$$\sqrt{ \frac{ 2 \times 71.6 }{ 9.8 } }$$

Evaluate

$$\frac{2\sqrt{179}}{7}\approx 3.822596617$$

Solution Steps

Multiply 2 and 71.6 to get 143.2.

$$\sqrt{\frac{143.2}{9.8}}$$

Expand \frac{143.2}{9.8} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{1432}{98}}$$

Reduce the fraction \frac{1432}{98} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{716}{49}}$$

Rewrite the square root of the division \sqrt{\frac{716}{49}} as the division of square roots \frac{\sqrt{716}}{\sqrt{49}}.

$$\frac{\sqrt{716}}{\sqrt{49}}$$

Factor 716=2^{2}\times 179. Rewrite the square root of the product \sqrt{2^{2}\times 179} as the product of square roots \sqrt{2^{2}}\sqrt{179}. Take the square root of 2^{2}.

$$\frac{2\sqrt{179}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{179}}{7}$$