How to find square root of 243/867 and 1183/1053

square root of 243/867 is given by;
$\sqrt{\frac{243}{867}} = \frac{\sqrt{3\times 3\times 3\times 3\times 3}}{\sqrt{3\times 17\times 17}} = \frac{\sqrt{3^2\times 3^2\times 3}}{\sqrt{3\times {17}^2}} = \frac{3\times 3\sqrt{3}}{17\sqrt{3}} = \frac{9}{17}$
And square root of 1183/1053  is given by;
$\sqrt{\frac{1183}{1053}} = \frac{\sqrt{7\times 13\times 13}}{\sqrt{3\times 3\times 3\times 3\times 13}} = \frac{\sqrt{7\times {13}^2}}{\sqrt{3^2\times 3^2\times 13}} = \frac{13\sqrt{7}}{3\times 3\sqrt{13}} = \frac{13\sqrt{7}}{9\sqrt{13}}$