Confusion on when to put ± sign

The $\pm$ sign definitely can cause a lot of confusion for students. For starters,

$|x|=\pm{x}$
$x^{2}={|x|}^2$

and the list goes on.

So my focus today is to explain when to put $\pm$ while dealing with $\sqrt{ }$ . First, lets recognise a few things.

$x=\sqrt{9}$ : This gives us $x=3$

$x^{2}=9$ : This gives us $x=\pm{3}$

Yes, the square-root can be raised to a square for the x, but notice the difference in answer in both cases. The former is a $+3$ while the latter has $-3$ too. This is because the square-root is always a positive square-root and does not return $\pm{ }$ . On the other hand, $x^{2}={|x|}^2$ and the $|x|=\pm{x}$ which causes the $\pm{ }$ .

So next time, please be alert when you introduce the $\pm{ }$ .

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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List of Great and Helpful Math Articles – The Culture
[…] Fallacies #1 16. Classical Mathematical Fallacies #2 17. Classical Mathematical Fallacies #3 18. Confusion on when to put ± sign 19. Difference between H1 and H2 Math 20. Partial Fractions made easy 21. The Modulus Sign #1 22. […]
May 1st, 2016 04:07 PM

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Confusion on when to put ± sign

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