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Question Number 184251 by Shrinava last updated on 04/Jan/23

$$\mathrm{If}\mathrm{x}\sqrt{\mathrm{y}}=2904$$$$\mathrm{Find}:\mathrm{y}=?$$

Answered by SEKRET last updated on 04/Jan/23

$$\mathbf{x}\cdot \sqrt{\mathbf{y}}=2^3\cdot 3\cdot {11}^2$$$$\{\begin{array}{l}\mathbf{x}=2\\ \sqrt{\mathbf{y}}=2^2\cdot {11}^2\cdot 3\end{array}\{\begin{array}{l}\mathbf{x}=2^2\\ \sqrt{\mathbf{y}}=2\cdot 3\cdot {11}^2\end{array}\{\begin{array}{l}\mathbf{x}=2^3\\ \sqrt{\mathbf{y}}=3\cdot {11}^2\end{array}$$$$\{\begin{array}{l}\mathbf{x}=2^2\cdot 3\cdot {11}^2\\ \sqrt{\mathbf{y}}=2\end{array}\{\begin{array}{l}\mathbf{x}=2\cdot 3\cdot {11}^2\\ \sqrt{\mathbf{y}}=2^2\end{array}\{\begin{array}{l}\mathbf{x}=3\cdot {11}^2\\ \sqrt{\mathbf{y}}=2^3\end{array}$$$$\{\begin{array}{l}\mathbf{x}=3\\ \sqrt{\mathbf{y}}=2^3\cdot {11}^2\end{array}\{\begin{array}{l}\mathbf{x}=11\\ \sqrt{\mathbf{y}}=2^3\cdot 11\cdot 3\end{array}\{\begin{array}{l}\mathbf{x}={11}^2\\ \sqrt{\mathbf{y}}=2^3\cdot 3\end{array}$$$$\{\begin{array}{l}\mathbf{x}=2^3\cdot {11}^2\\ \sqrt{\mathbf{y}}=3\end{array}\{\begin{array}{l}\mathbf{x}=2^3\cdot 11\cdot 3\\ \sqrt{\mathbf{y}}=11\end{array}\{\begin{array}{l}\mathbf{x}=2^3\cdot 3\\ \sqrt{\mathbf{y}}={11}^2\end{array}$$$$\{\begin{array}{l}\mathbf{x}=1\\ \sqrt{\mathbf{y}}=2904\end{array}\{\begin{array}{l}\mathbf{x}=2904\\ \sqrt{\mathbf{y}}=1\end{array}$$$$\{\begin{array}{l}\mathbf{x}=2\cdot 3\\ \sqrt{\mathbf{y}}=2^2\cdot {11}^2\end{array}\{\begin{array}{l}\mathbf{x}=2^2\cdot 3\\ \sqrt{\mathbf{y}}=2\cdot {11}^2\end{array}\{\begin{array}{l}\mathbf{x}=2^3\cdot 3\\ \sqrt{\mathbf{y}}={11}^2\end{array}$$$$\{\begin{array}{l}\mathbf{x}=2^2\cdot {11}^2\\ \sqrt{\mathbf{y}}=2\cdot 3\end{array}\{\begin{array}{l}\mathbf{x}=2\cdot {11}^{22}\\ \sqrt{\mathbf{y}}=2^2\cdot 3\end{array}\{\begin{array}{l}\mathbf{x}={11}^2\\ \sqrt{\mathbf{y}}=2^3\cdot 3\end{array}$$$$........$$$$.............$$

Answered by SEKRET last updated on 04/Jan/23

$$\sqrt{\mathbf{y}}=\frac{2904}{\mathbf{x}}\mathbf{x}\ne 0$$$$\mathbf{y}=\frac{{2904}^2}{{\mathbf{x}}^2}$$

Answered by mr W last updated on 04/Jan/23

$$forx,y\in Z,thereare24solutions.$$$$y={\left(\frac{2^3\times 3\times {11}^2}{x}\right)}^2$$

Answered by Ml last updated on 04/Jan/23

$$\mathrm{x}=2904$$$$\mathrm{y}=1$$

Answered by Rasheed.Sindhi last updated on 04/Jan/23

$$x\sqrt{y}=2^3\cdot 3\cdot {11}^2$$$$yisperfectsquare\mathrm{\&}divisorof2904$$$$y=1,2^2,{11}^2,{\left(2\times 11\right)}^2$$$$=1,4,121,484$$

Commented by mr W last updated on 04/Jan/23

$$pleaserechecksir!$$$$ithinkymustnotbedivisorof2904.$$$$\sqrt{y}isdivisorof2904.since2904has$$$$24divisors,\sqrt{y}mayhave24possible$$$$values,thereforeymayalsohave$$$$24possiblevalues,notonly5values.$$$$forexampley={2904}^{2}isalsoavalid$$$$solution.$$

Commented by Rasheed.Sindhi last updated on 04/Jan/23

$${You}^{\prime }reright\mathit{s}\mathit{i}\mathit{r}!{It}^{\prime }smymistake!$$

Answered by Frix last updated on 04/Jan/23

$$x\sqrt{y}=2904$$$$\sqrt{y}=\frac{2904}{x}$$$$y={\left(\frac{2904}{x}\right)}^2$$$$\mathrm{I}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{get}\mathrm{all}\mathrm{the}\mathrm{complicated}\mathrm{answers}.$$$${\mathrm{It}}^{\prime }\mathrm{s}\mathrm{like}$$$$a+\frac{b}{2}=15$$$$\mathrm{Find}:b=?$$$$\mathrm{What}\mathrm{am}\mathrm{I}\mathrm{missing}?$$

Commented by Frix last updated on 04/Jan/23

$$\mathrm{People}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{answer}\mathrm{given}\mathrm{questions}\mathrm{but}$$$$\mathrm{instead}\mathrm{adding}\mathrm{something}\mathrm{new}\mathrm{to}\mathrm{questions}$$$$\mathrm{before}\mathrm{solving}\mathrm{them}?!?$$

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