When solving an example like the attached picture, we say x is +/- answer.
But if the equation is $$x+4=\sqrt{9/16}$$ Are we supposed to write plus or minus in this case too?
Do we still need to write plus or minus when solving this equation including a square root?
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1Writing $\sqrt{x^2} = \pm \sqrt 4$ in the image is not quite right -- the $\sqrt{\phantom 4}$ notation always means the _positive_ square root, and applying the $\sqrt{\phantom 4}$ function on both sides of the equation $x^2=4$ cannot suddenly make a minus appear out of nowhere. In the _next_ step, $\sqrt{x^2}=\sqrt 4$ should have been rewritten to $|x|=\sqrt 4$ which is the same as $x=\pm 2$. – 2017-02-06
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0If you had $(x+4)^2=9/16$ then yes, otherwise no. – 2017-02-06
1 Answers
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No. $\sqrt{\frac9{16}}$ is just the non-negative real number $\alpha$ such that $\alpha^2=\frac9{16}$, and that's why the solution to $x^2=4$ is $x=\pm\sqrt4$. The expression $x+4=\sqrt{\frac9{16}}$ just means $x+4=\frac34$.