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Express \(\sqrt{x} \div\sqrt{y}\) as a common fraction, given: \(\frac{ {\left( \frac{1}{2} \right)}^2 + {\left( \frac{1}{3} \right)}^2 }{ {\left( \frac{1}{4} \right)}^2 + {\left( \frac{1}{5} \right)}^2} = \frac{13x}{41y} \)

 Feb 21, 2021

Best Answer 

 #1
avatar+30881 
+2

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

 Feb 22, 2021
 #1
avatar+30881 
+2
Best Answer

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

ElectricPavlov Feb 22, 2021

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