document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #396035 by jsmallt9(3758) $\"\"$ $\"About$

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$\"-sqrt%28133%29\"$
\n" ); document.write( "Every positive number, like 133, has two square roots, a positive one and a negative one. $\"sqrt%28133%29\"$ is how we refer to the positive square root of 133 and $\"-sqrt%28133%29\"$ is how we refer to the negative one. If we want to refer to both we use a \"plus or minus\" symbol: $\"0+%2B-+sqrt%28133%29\"$ (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.)

\n" ); document.write( "So we can already rule out answer \"c\" since $\"-sqrt%28133%29\"$ 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\"

\n" ); document.write( "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):
\n" ); document.write( " $\"sqrt%28100%29+=+10\"$
\n" ); document.write( " $\"sqrt%28121%29+=+11\"$
\n" ); document.write( " $\"sqrt%28144%29+=+12\"$
\n" ); document.write( "Since 133 is between 121 and 144, $\"sqrt%28133%29\"$ is between $\"sqrt%28121%29\"$ (or 11) and $\"sqrt%28144%29\"$ (or 12). So $\"-sqrt%28133%29\"$ is a negative number between -11 and -12.

\n" ); document.write( "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\". \n" ); document.write( "

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