Solve sqrt{78/4.9}

$$\sqrt { \frac { 78 } { 4.9 } }$$

Evaluate

$$\frac{2\sqrt{195}}{7}\approx 3.98978287$$

Solution Steps

Expand \frac{78}{4.9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{780}{49}}$$

Rewrite the square root of the division \sqrt{\frac{780}{49}} as the division of square roots \frac{\sqrt{780}}{\sqrt{49}}.

$$\frac{\sqrt{780}}{\sqrt{49}}$$

Factor 780=2^{2}\times 195. Rewrite the square root of the product \sqrt{2^{2}\times 195} as the product of square roots \sqrt{2^{2}}\sqrt{195}. Take the square root of 2^{2}.

$$\frac{2\sqrt{195}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{195}}{7}$$