+236 Express \(\sqrt{x} \div\sqrt{y}\) as a common fraction, given: \(\frac{ {\left( \frac{1}{2} \right)}^2 + {\left( \frac{1}{3} \right)}^2 }{ {\left( \frac{1}{4} \right)}^2 + {\left( \frac{1}{5} \right)}^2} = \frac{13x}{41y} \)
+36916 Numerator 1/4 + 1/9 = 13/36
denominator 1/16 + 1/25 = 41/400
13/36 * 400 / 41 = 5200/1476 = 1 300/369 = 13/x / 41y
1300/369 * 41/13 = x/y = 100/9
take sqrt of both sides sqrt x / sqrt y = 10/3
+36916 Numerator 1/4 + 1/9 = 13/36
denominator 1/16 + 1/25 = 41/400
13/36 * 400 / 41 = 5200/1476 = 1 300/369 = 13/x / 41y
1300/369 * 41/13 = x/y = 100/9
take sqrt of both sides sqrt x / sqrt y = 10/3
