â(289) = 17, so |8 - â(289)| = |8 - 17| = |-9| = 9. Note that âx is defined to be the POSITIVE number whose square is x, so the expression |8-â289| has a unique well-defined value.
(I have assumed your square root is the principle square root meaning it only takes the positive root and not the negative one otherwise â289 equals both 17 and -17)
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Verified answer
It's easy enough to just change this to |8 - 17| = |-9| = 9, but we're specifically being asked to "USE THE DEFINITION of absolute value".
The absolute value is formally defined as
|a| = √(a^2)
So here we have
√[(8 - √289)^2]
√[64 - 16√289 + 289]
√(353 - 16*17)
√81 = 9
Another way to define absolute value is that
|a| = a for a>=0, and |a| = -a for a<=0.
So you could also say that since the inside is √64 - √289 < 0, then the absolute value is negative of this, or -(8 - √289) = (√289) - 8 = 17 - 8 = 9.
Use whichever definition you were taught in your class or text book.
â(289) = 17, so |8 - â(289)| = |8 - 17| = |-9| = 9. Note that âx is defined to be the POSITIVE number whose square is x, so the expression |8-â289| has a unique well-defined value.
|8 - â289| = |8 + 17| = |25| = 25
(I have assumed your square root is the principle square root meaning it only takes the positive root and not the negative one otherwise â289 equals both 17 and -17)
â289 = positive or negative 17.
considering positive 17, |8 - 17| = 9
considering negative 17, |8 - (-17)| = 25.
Ok. Now what do I do with the answer? Is this a riddle or something?