Use the definition of absolute value to fine |8-√289|.?

Question

Use the definition of absolute value to fine |8-√289|.?

Answer 1

Ok.  Now what do I do with the answer?  Is this a riddle or something?

Answer 2

√289 = positive or negative 17.

considering positive 17, |8 - 17| = 9

considering negative 17, |8 - (-17)| = 25.

Answer 3

|8 - √289| = |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 √289 equals both 17 and -17)

Answer 4

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 -  Ã¢ÂˆÂš289)^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.

Answer 5

√(289) = 17, so |8 - √(289)| = |8 - 17| = |-9| = 9.  Note that √x is defined to be the POSITIVE number whose square is x, so the expression |8-√289| has a unique well-defined value.