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I want to solve for $x$

Here's the question

$$\large \sqrt{12} - \sqrt[3\leftroot1]{720} = \sqrt{x}$$

I need to find the value of $x$

Help!

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    $\begingroup$ Hint: how can you get rid of the square root from $\sqrt{x}$? $\endgroup$
    – N. S.
    Feb 12, 2013 at 16:01
  • $\begingroup$ yeh i thought of making the base equal $\endgroup$
    – gandhigcpp
    Feb 12, 2013 at 16:03
  • $\begingroup$ making the base equal and solving gets long & probamatic $\endgroup$
    – gandhigcpp
    Feb 12, 2013 at 16:16
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    $\begingroup$ Note that $\sqrt{12}-\sqrt[3]{720}\approx-5.5<0$. While this suggests $x\approx(-5.5)^2\approx30.2$, by definition the square root of a positive real is positive. Hence there is no solution. $\endgroup$ Feb 12, 2013 at 16:36

1 Answer 1

3
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The equation you gave is $$ \sqrt{12}-\sqrt[3]{720}=\sqrt{x} $$ The left side of this equation is less than $0$. The positive root of $x$ can never be less than $0$, so there's no solution.

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  • $\begingroup$ so there's no need for actually solving this $\endgroup$
    – gandhigcpp
    Feb 12, 2013 at 17:08
  • $\begingroup$ on solving the left hand side i got 8.96 ~ is int like the answer be 3 $\endgroup$
    – gandhigcpp
    Feb 12, 2013 at 17:10
  • $\begingroup$ one more thing since i expected this question to be solved in a minute or so how can i do for other questions like these the thing is that it is easy to calculate using calculator $\endgroup$
    – gandhigcpp
    Feb 13, 2013 at 13:23

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