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i want to clarify whether this result is correct.is it true ?anyone please say

2007-07-02 04:41:09 · 4 answers · asked by Anonymous in Science & Mathematics Mathematics

4 answers

You can only obtain a real value if the radicand (the expression inside the radical) is positive. The result is true.

Now, if we are working on complex numbers, yet a & b are real numbers, even if some of them are negative, the expression is still valid.
If you have no idea what complex numbers are yet, disregard my last statement. (I do not know what grade you are, if you are a student.)

The positivity or negativity of a & b depends on whether you are working only on reals or you are working with complex numbers.
d:

2007-07-02 04:46:49 · answer #1 · answered by Alam Ko Iyan 7 · 0 0

If a and b are negative, we are dealing with complex numbers for their square roots. And no, it is not true for complex numbers a and b that we can always say sqrt(ab) = sqrt(a) * sqrt(b). The reason we encounter a problem is that there is not a clear-cut convention of which solution of x^2 = a should be chosen as the square root of a. In working with positive real numbers, we have the convention (and that's all it is, just a convention) that we take the positive square root, and then things work out. But if you think of numbers as having two square roots, it's not even true for real square roots that sqrt(ab) = sqrt(a) * sqrt(b). Suppose I took a = 4 and b = 9, and then chose 2 as the square root of 4, -3 as the square root of 9, and 6 as the square root of 36? Boom, it doesn't work out!

The reason there is no convention in the case of the complex numbers is that it's just very unclear which of the two square roots you should choose. Consider -2i, for example. It has two square roots, 1-i and -1+i. Which is better? Beats me.

2007-07-02 11:27:25 · answer #2 · answered by jw 3 · 0 0

sq root (ab)=sqroot(a)sq root(b)only when a or b is positive..

It is incorrect.
sqrt(ab) = sqrt(a)*sqrt(b) is true in all cases:
a and b both both positive
a and b both negative
a positive and b negative
a negative and b positive

In the first cases the result will be a real number
In the last two cases the result will be an imaginary number

2007-07-02 04:51:36 · answer #3 · answered by ironduke8159 7 · 0 0

yes it's true...

2007-07-02 04:46:21 · answer #4 · answered by fofo m 3 · 0 0

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