SOLUTION: estimate each square root to the nearest whole number. -/133 / is the square root symbol answers a:-12 b:-66.5 c:13 d:-11.5

Question 628991: estimate each square root to the nearest whole number. -/133 / is the square root symbol answers a:-12 b:-66.5 c:13 d:-11.5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Every positive number, like 133, has two square roots, a positive one and a negative one. is how we refer to the positive square root of 133 and is how we refer to the negative one. If we want to refer to both we use a "plus or minus" symbol: (Note: The zero is not usually used. The zero is only there because a flaw in algebra.com's drawing software will not draw the "plus or minus" symbol without something in front of it.)

So we can already rule out answer "c" since is a reference to a negative number. And we can also rule out answers "b" and "d" because the problem asks for a whole number solution and -66.5 and -11.5 are not whole numbers. SO the answer must be "a"

If we were not able to rule out all but one of the answers, or if it had not been a multiple choice problem, here is what we would do to figure out the right answer: lets think of some nearby numbers whose square roots we know (i.e. perfect squares):

Since 133 is between 121 and 144, is between (or 11) and (or 12). So is a negative number between -11 and -12.

P.S. Technically, -12 is not a whole number either. Whole numbers are 0, 1, 2, 3, .... They do not include negative numbers. It is a common mistake to think of "whole numbers" as "numbers which have no fractional parts." But the proper term for "numbers which have no fractional parts" is "integer".
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