Find the square roots of the followings(i)$\frac{225}{441}$

The factors of 225 is $5\times 5\times 3\times 3$ and the factors of 441 is $3\times 3\times 7\times 7$. Then,

$\frac{225}{441}=\frac{5\times 5\times 3\times 3}{3\times 3\times 7\times 7}$

Taking square roots both sides,

$\sqrt{\frac{225}{441}}=\sqrt{\frac{5\times 5\times 3\times 3}{3\times 3\times 7\times 7}}$

$=\sqrt{\frac{5^2\times 3^2}{3^2\times 7^2}}$

$=\sqrt{{\left(\frac{5\times 3}{3\times 7}\right)}^2}$

$=\frac{5\times 3}{3\times 7}$

$=\frac{15}{21}$

Therefore, the square root of $\frac{225}{441}$ is $\frac{15}{21}$.