Solve sqrt{1764/2197}

$$\sqrt { \frac { 1764 } { 2197 } }$$

Evaluate

$$\frac{42\sqrt{13}}{169}\approx 0.896054163$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1764}{2197}} as the division of square roots \frac{\sqrt{1764}}{\sqrt{2197}}.

$$\frac{\sqrt{1764}}{\sqrt{2197}}$$

Calculate the square root of 1764 and get 42.

$$\frac{42}{\sqrt{2197}}$$

Factor 2197=13^{2}\times 13. Rewrite the square root of the product \sqrt{13^{2}\times 13} as the product of square roots \sqrt{13^{2}}\sqrt{13}. Take the square root of 13^{2}.

$$\frac{42}{13\sqrt{13}}$$

Rationalize the denominator of \frac{42}{13\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{42\sqrt{13}}{13\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{42\sqrt{13}}{13\times 13}$$

Multiply 13 and 13 to get 169.

$$\frac{42\sqrt{13}}{169}$$