Basic math question

[2014DMD]

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I think this is one of those questions too basic even for any of the study guides to address.

say I'm solving an equation for x, and I have something on each side of the =. Can I square both sides?? I know I can multiply both sides by any number (long as I do the same to both sides), but can I square or raise both sides to an exponent - is that a valid operation??

Again, this is basic, but any help appreciated.

Cheers!

 

[house2272000]

as long as you do the same thing to both side you are fine. Like square both the sides of the = sign you are fine.

 

[jay47]

I think this is one of those questions too basic even for any of the study guides to address.

say I'm solving an equation for x, and I have something on each side of the =. Can I square both sides?? I know I can multiply both sides by any number (long as I do the same to both sides), but can I square or raise both sides to an exponent - is that a valid operation??

Again, this is basic, but any help appreciated.

Cheers!

Of course you can! All you have to remember is the golden rule of algebra: What you do to one side of an equation, do to the other.

Here's more on the topic from a great source: http://www.purplemath.com/modules/solverad.htm

 

[DO2Be2013]

Like everyone has said, yes you can square both sides. In algebra it's helpful to mentally replace variable expressions with real numbers and then test your procedure. For example, you know that 3 + 1 = 2 + 2. So as long as you square the entire expressions (as though they were in parentheses) you're fine... (3 + 1)^2 = (2 + 2)^2. But what you cannot do is distribute a "squared" across individual terms... shown by the fact that 3^2 + 1^2 does not equal 2^2 + 2^2. My old algebra students would always make the mistake of squaring something like (x + 3) on one side of an equation and giving x^2 + 9 as the result, when really you can't just square each term you have to multiply the whole expression by itself, getting (x + 3)(x + 3) which is really x^2 + 6x + 9. Hope that helps.

You can perform any operation on both sides of the equal sign... including powers, radicals, logarithms, etc. You aren't limited to the four basic operations.

 

[2014DMD]

thanks to all!!

 

[Streetwolf]

I doubt this would appear on the DAT but be careful about certain operations. Always go back and CHECK YOUR SOLUTIONS IN THE ORIGINAL PROBLEM.

Sometimes you get extraneous roots. These usually can happen when you work with square roots and exponentials (logs).

 

[Pwn]

No, actually yes but be careful. You can get false solutions doing this.

-3 = 3 (Not true)
Square
9=9 (True)
wait wut

 

[DO2Be2013]

No, actually yes but be careful. You can get false solutions doing this.

-3 = 3 (Not true)
Square
9=9 (True)
wait wut

If you're starting with an "equation" where the two sides aren't actually equal, like -3 = 3 then of course whatever solution(s) you get will be faulty. If the two sides are truly equal (i.e., an equation) then squaring both sides will always produce a valid equation.

 

[Streetwolf]

If you're starting with an "equation" where the two sides aren't actually equal, like -3 = 3 then of course whatever solution(s) you get will be faulty. If the two sides are truly equal (i.e., an equation) then squaring both sides will always produce a valid equation.

sqrt(x) = -3

Square both sides:

x = 9

Check your answer:

sqrt(9) = 3

Doesn't work. Can't use the negative for the square root function.