Rearrange Formulae When Subject Appears As A Square

[nortski]

I have a simple looking formula that I just can't seem to rearrange to get the correct answer.
Make y the subject of x = y² / 4

According to my revision guide I should deal with the fraction first:
4x = y²

All that is left to do is square root both sides:
y = +- [MATH]\sqrt{4x}[/MATH]
However the answer given is:
y = +- 2[MATH]\sqrt{x}[/MATH]
So am I supposed to be square rooting the 4 and x separately instead as a single term?

 

[pka]

Would it surprise you to learn that \(\bf\pm\sqrt{4x}=\pm 2\sqrt{x}~?\)
I will say that the second is the preferred form.

 

[Mr. Bland]

The reason this works is because, generally speaking, [MATH]\sqrt{ab} = \sqrt{a} * \sqrt{b}[/MATH]. In your case, [MATH]\sqrt{4x} = \sqrt{4} * \sqrt{x}[/MATH].

 

[nortski]

Would y = ±√4x be marked as correct in an exam?

 

[HallsofIvy]

Apparently whoever gave you this problem expects you to know that \(\displaystyle \sqrt{ab}= \sqrt{a}\sqrt{b}\). If you do not know rhat, do you at least know that \(\displaystyle (\sqrt{a})^2= (\sqrt{a})(\sqrt{a})= a\)?

 

[nortski]

Apparently whoever gave you this problem expects you to know that \(\displaystyle \sqrt{ab}= \sqrt{a}\sqrt{b}\). If you do not know rhat, do you at least know that \(\displaystyle (\sqrt{a})^2= (\sqrt{a})(\sqrt{a})= a\)?

I have come across this yes, but there's been a lot to take in and things take a little longer to stick these days lol

 

[Dr.Peterson]

Would y = ±√4x be marked as correct in an exam?

That is a correct answer, but would lose points if either the exam included instructions that the answer should be fully simplified, or that was a general rule in the class.

Properly speaking, by the way, if you can't put a bar over the radicand when typing, you should write it as y = ±√(4x) to show that it is not only the 4 that is under the radical.