GMATprep: square root

IMO E

√(x^2)=|x|. its a formula.

otherwise put values
x=-1 ,√(x^2)=1
√(x^2)/x=-1= |x|/x
put x=1

√(x^2)=1
√(x^2)/x=1=|x|/x

Hey tohellandback

√(x^2)=|x|. its a formula.

otherwise put values
x=-1 ,√(x^2)=1
√(x^2)/x=-1= |x|/x
put x=1

√(x^2)=1
√(x^2)/x=1=|x|/x

Can u explain in detail that how this is a formula???

abhinav,
I know what you are thinking

√(x^2) should be x and -x
well thats true. but thing is it is defined that way

https://en.wikipedia.org/wiki/Square_root
and in fact if we go deeper, the roots of the eq x^2=a are is are+√a and -√a because √x means the positive square root.
it's a convention because usually we are looking for the positive solution
But anyways, if you are looking for a proof then I don't have it.

Answer should be 1.

Square root of any positive number is always positive.. (You can read OG11 for this.. I think page number 114). Long back, I had committed the same mistake as you guys are doing.. so just keep it simple.. in GMAT principal square root of a number denoted by that "root" sign is positive..
root(x^2) is x and that divided by x is 1

so C is the answer.

dumb.doofus wrote:Answer should be 1.

Square root of any positive number is always positive.. (You can read OG11 for this.. I think page number 114). Long back, I had committed the same mistake as you guys are doing.. so just keep it simple.. in GMAT principal square root of a number denoted by that "root" sign is positive..
root(x^2) is x and that divided by x is 1

so C is the answer.

I guess you should read this:
https://www.beatthegmat.com/if-x-0-then- ... 14328.html
thre is one more post by Ian..I don't know where. if someone knows. please post the link

C

I replaced x:

If x ≠ 0, then √(x^2)/x =

x=10

10^2=100
√100=10

10/10

or

x=-10

-10^2=100
√100=10

10/10

or

x=2

2^2= 4
√4=2

2/2

hazpazfaz wrote:C

I replaced x:

If x ≠ 0, then √(x^2)/x =

x=10

10^2=100
√100=10

10/10

or

x=-10

-10^2=100
√100=10

10/10

or

x=2

2^2= 4
√4=2

2/2

if you replace X = -10 the result is
sqrt(-10^ 2)/ (-10) = sqrt(100)/(-10) = 10/-10 = -1

so C cannot be the answer
tohellandback is right the answer to this question is E, using the formula he provided.

E.
square root of x^2 is abs of x.
This is not debatable, it is a formula

Yes.. I will go for E

sqrt( x^2) = |x|

I follow your guys logic...

Now maybe my algebra is wrong.

But...

Why can't we just simplify the equation?

isn't the sqrt(x) = x^(1/2)

Now that being said, wouldn't the sqrt(x^2) = x^2/2 = x

Then x / x = 1 ???

OR

what if you just square the top and bottom of the equation to get rid of the sqrt?

Then aren't we left with x^2/x^2 = 1


This a good question, I'm just throwing my thoughts out there...

Agree/disagree?

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Now that being said, wouldn't the sqrt(x^2) = x^2/2 = x

the answer is no because:

sqrt(x^2) = sqrt (1^2)x sqr (x^2/2) = x
OR
sqrt(x^2) = sqrt (-1)^2)x sqr (x^2/2) = -x

x and -x are conventionally written abs x