- #1
Ali Asadullah
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Please tell me
Sqrt (x^2)=______ For All Real Numbers
(Sqrt x^2)=______ For All Real Numbers
Thank YOu..!
Sqrt (x^2)=______ For All Real Numbers
(Sqrt x^2)=______ For All Real Numbers
Thank YOu..!
The first one is defined for all real numbers.Ali Asadullah said:Please tell me
Sqrt (x^2)=______ For All Real Numbers
(Sqrt x^2)=______ For All Real Numbers
Thank YOu..!
Ali Asadullah said:Thank You Mark44
Please also tell me whether they are equal to each other or not?
Ali Asadullah said:Sir let (sqrt x)^2=x
And substitute x=-1, then we would have (i)^2=-1.
Is it right?
MathematicalPhysicist said:I have seen such notation of \sqrt(-1) in textbooks which use for indices also i and j.
It's really a matter of notation.
For example Principles of Algebraic Geometry by Harris uses \sqrt(-1) instead of i.
Sqrt(x^2) represents the square root of the entire expression x^2. This means that any negative value of x will result in a positive value for Sqrt(x^2). On the other hand, (Sqrt x)^2 represents the square of the square root of x. This means that any negative value of x will remain negative when squared.
The use of parentheses in (Sqrt x)^2 is important because it indicates that the square root operation is being applied to x before it is squared. Without the parentheses, the equation would be interpreted as Sqrt(x) squared, which is mathematically incorrect.
The domain of both expressions is all real numbers. This means that any real number can be substituted for x and the expressions will still be valid.
Yes, they can have different values. This is because the expressions are not equivalent. Sqrt(x^2) simplifies to the absolute value of x, while (Sqrt x)^2 simplifies to just x. Therefore, their values will only be the same when x is a non-negative number.
Sqrt(x^2) can be simplified to the absolute value of x and (Sqrt x)^2 can be simplified to just x. However, if we want to simplify further, we can substitute in a value for x and evaluate the expressions. For example, if x = 9, then Sqrt(x^2) = 9 and (Sqrt x)^2 = 9. Therefore, both expressions simplify to the same value of 9.