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03 Apr 2014, 05:39
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If √4 =x, what is x?
In the above example, x = 2, since (2)(2)= 4. While it is true that (-2)(-2) =4, the GMAT
follows the standard convention of mathematics. When we take an even root (a square
root, a 4th root, a 6th root, etc.), a radical sign means ONLY the nonnegative root of a
number. Thus, the number 2 is the only solution for x. -2 is NOT a solution for this problem.
When you see a square root symbol on the GMAT, think only the positive root. (In
contrast, when you decide to unsquare an equation with even exponents, you must consider
both positive and: negative solutions. For instance, the equation x2 = 4 haS two solutions:
x = 2 and x:; -2.)
.
.
.
the above is written in Manhattan Number properties guide book. However in the chapter for exponents they are also mentioning that If X 2 = 16, is X equal to 4?
Your initial inclination is probably to say yes. However, x may not be 4; it may be -4. Thus,
we cannot answer the question without additional information. We must be told that x is
positive in order to affirm that x is 4. Beware whenever you see aneven exponent on the
test.
I am confused if I need to go by this rule or every time I should consider both the sign (+, - ) in all cases. please help.
In the above example, x = 2, since (2)(2)= 4. While it is true that (-2)(-2) =4, the GMAT
follows the standard convention of mathematics. When we take an even root (a square
root, a 4th root, a 6th root, etc.), a radical sign means ONLY the nonnegative root of a
number. Thus, the number 2 is the only solution for x. -2 is NOT a solution for this problem.
When you see a square root symbol on the GMAT, think only the positive root. (In
contrast, when you decide to unsquare an equation with even exponents, you must consider
both positive and: negative solutions. For instance, the equation x2 = 4 haS two solutions:
x = 2 and x:; -2.)
.
.
.
the above is written in Manhattan Number properties guide book. However in the chapter for exponents they are also mentioning that If X 2 = 16, is X equal to 4?
Your initial inclination is probably to say yes. However, x may not be 4; it may be -4. Thus,
we cannot answer the question without additional information. We must be told that x is
positive in order to affirm that x is 4. Beware whenever you see aneven exponent on the
test.
I am confused if I need to go by this rule or every time I should consider both the sign (+, - ) in all cases. please help.
03 Apr 2014, 19:15
Kudos
Bookmarks
joydrath2013
A positive number has two square roots: a positive square root (also called principal square root) and a negative square root. they are depicted as \(\sqrt{x}\) and \(-\sqrt{x}\). So by convention, \(\sqrt{x}\) implies we are talking about only the positive square root.
On the other hand, \(x^2 = 4\) has two solutions: x = 2 or -2
03 Apr 2014, 21:03
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Bookmarks
hi,
let me simplify my initial question. if in the GMAT exam, question has come like this : √4 =x, what is x?
what will be answer/answers ?
let me simplify my initial question. if in the GMAT exam, question has come like this : √4 =x, what is x?
what will be answer/answers ?
