What is the value of y?

Question

What is the value of  y ?

(1)  y^2 = 9 
(2)  y=\sqrt{9}

chetan2u · Answer

What is the value of  y ?

(1)  y^2 = 9=3^2=(-3)^2 
So y can be 3 or -3.
Insufficient

(2)  y=\sqrt{9} 
 Square root is always positive.  So  y=\sqrt{9}=3 
Sufficient

B

BrentGMATPrepNow · Answer

Target question :    What is the value of  y ?

Statement 1 :  y^2 = 9  
Since  3^2 = 9  and  (-3)^2 = 9 , we can see there are two answers to the target question:  y = 3  and  y = -3  
Statement 1 is NOT SUFFICIENT

Statement 2 :  y=\sqrt{9}  
The key concept here is that, although there are two values (3 and -3) that, when squared, yield 9, the square root   notation   tells us to take only the  positive  root.
So,  y = 3  
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

SUMMARY OF ABOVE CONCEPTS
 https://i.imgur.com/g1WRrax.png

rahulp11 · Answer

BrentGMATPrepNow  could you please explain the above notation effect, if the equation was  \sqrt{x^2} = 19  ;

Typically, the solution would be as follows

If  \sqrt{x^2} = 19

then  |x|  = 19

i.e.  x  = +19 or -19

but considering the impact of the notation, should we consider only the positive value of  x  i.e  x  = +19 ?

I am unsure about proving sufficiency by my understanding of the solutions here and from another similar problem linked below
 https://gmatclub.com/forum/what-is-the-value-of-x-1-x-2-19-2-19-2-x-348768.html

It would really help if you can explain by considering the perspective of both the problems.

My understanding of why  \sqrt{x^2} = 19  can take both positive and negative values of  x  is because we have an even power(square) within the radical, therefore, the value under the radical is always positive. Whereas in the case of  19 = \sqrt{x} ,  x  can take only positive values as square root of negative number is not a real number.

Is the above approach correct and valid for determining sufficiency?

Thanks
RP

MBAHOUSE · Answer

Some students make the mistake thinking that the square root of an number gives a positive and negative answer.
No, a square root of a number occupies only one point in the real number line.
The statement 1 results in two number because the statement presents an incomplete quadratic equation that is a parabola with Δ > 0 with two real roots.

BrentGMATPrepNow · Answer

The square root notation tells to take only the positive root. 
So, the equation  \sqrt{x^2} = 19  follows this rule because it's not suggesting that  \sqrt{x^2} = -19

What is the value of y?

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