Question

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

Answer 1

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;
$\sqrt{\frac{1183}{1053}}=\frac{\sqrt{7\times 13\times 13}}{\sqrt{3\times 3\times 3\times 3\times 13}}=\frac{\sqrt{7\times {13}^2}}{\sqrt{3^2\times 3^2\times 13}}=\frac{13\sqrt{7}}{3\times 3\sqrt{13}}=\frac{13\sqrt{7}}{9\sqrt{13}}$