Solve sqrt{416/49}

$$\sqrt { 4 \frac { 16 } { 49 } }$$

Evaluate

$$\frac{2\sqrt{53}}{7}\approx 2.080031397$$

Solution Steps

Multiply 4 and 49 to get 196.

$$\sqrt{\frac{196+16}{49}}$$

Add 196 and 16 to get 212.

$$\sqrt{\frac{212}{49}}$$

Rewrite the square root of the division \sqrt{\frac{212}{49}} as the division of square roots \frac{\sqrt{212}}{\sqrt{49}}.

$$\frac{\sqrt{212}}{\sqrt{49}}$$

Factor 212=2^{2}\times 53. Rewrite the square root of the product \sqrt{2^{2}\times 53} as the product of square roots \sqrt{2^{2}}\sqrt{53}. Take the square root of 2^{2}.

$$\frac{2\sqrt{53}}{\sqrt{49}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{53}}{7}$$