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Solve the following. 225729−25144−1681\sqrt{\frac{225}{729}} - \sqrt{\frac{25}{144}} - \sqrt{\frac{16}{81}}729225​​−14425​​−8116​​​= ?
Question

Solve the following.
225729251441681\sqrt{\frac{225}{729}} - \sqrt{\frac{25}{144}} - \sqrt{\frac{16}{81}}​= ?

A.

(-11)/36

B.

(-5)/9

C.

(-20)/27

D.

(-7)/12

Correct option is A

225729251441681 152751249 5951249Find a common denominator (LCM of 9 and 12 is 36)=203615361636=20151636 =1136 Therefore, the value of the given expression is 1136.\sqrt{\frac{225}{729}} - \sqrt{\frac{25}{144}} - \sqrt{\frac{16}{81}}\\\ \\ \frac{15}{27} - \frac{5}{12} - \frac{4}{9}\\\ \\\frac{5}{9} - \frac{5}{12} - \frac{4}{9}\\\text {Find a common denominator (LCM of 9 and 12 is 36)}= \frac{20}{36} - \frac{15}{36} - \frac{16}{36} \\= \frac{20 - 15 - 16}{36}\\\ \\= \frac{-11}{36}\\\ \\\text{Therefore, the value of the given expression is } \frac{-11}{36}.\\​​

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