how is that sqrt ( (x-a)^2 ) = |x-a| Thanks

Question

how is that

sqrt ( (x-a)^2 ) = |x-a|

Thanks

tigershahkhan · Answer

is so because, sqrt is basically the same as saying (....)^1/2, so if you write the question again,
((x-a)^2)^1/2, thus the 2's cancel out and you get | x-a |, its absolute because sqrt can never be negative.

GMAT TIGER · Answer

This is basic but very important. the concept is that any square has 2 roots. for ex: if x^2 = 4
x could be 2 and -2. it can also be written as x = sqrt(4) or -sqrt(4). if x = sqrt(4), x = 2. if x = -sqrt(4), x = -2.

so if we apply the same rule in the above expression, we also get 2 roots for (x-a)^2: (1) sqrt {(x-a)^2} and (2) - . so

(1) sqrt {(x-a)^2} = lx-al
(2) -   = - lx-al

scthakur · Answer

sqrt((x-a)^2) can have two values, (x-a) or -(x-a) and hence |x-a|.

krishan · Answer

thanks for the clarification .

how is that sqrt ( (x-a)^2 ) = |x-a| Thanks

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