document.write( "Question 616442: please! help me with this => Simplify Remember to use absolute-value notation when necessary. If a root cannot be simplified, state this.\r
\n" ); document.write( "\n" ); document.write( " 1976 sqrt sign then (2a + b)^1976
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Algebra.Com's Answer #387715 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
If your expression is
\n" ); document.write( "\"root%281976%2C+%282a%2Bb%29%5E1976%29\"
\n" ); document.write( "then there is no square root sign. The proper name for what you call a \"square root sign\" is \"radical\". Radical symbols are used for all kinds of roots:
\n" ); document.write( "Square roots: \"sqrt%283x-6%29\" or \"root%282%2C+4x%2B4%29\"
\n" ); document.write( "Cube roots: \"root%283%2C+10x%2B23%29\"
\n" ); document.write( "4th roots: \"root%284%2C+-3x%2B90%29\"
\n" ); document.write( "etc.
\n" ); document.write( "Your expression is a 1976th root.

\n" ); document.write( "Since 1976 is an even number, a 1976th root is an even-numbered root. Even-numbered roots are not negative. So we must make sure that whatever answer we get, it must not turn out to be negative.

\n" ); document.write( "So how do we go about simplifying this? Well, once you understand what roots are, then this problem is extremely easy to simplify. A 1976th root is whatever you have to raise to the 1976th power to get the radicand as a result. (\"Radicand\" is the name for the expression inside a radical.) So
\n" ); document.write( "\"root%281976%2C+%282a%2Bb%29%5E1976%29\"
\n" ); document.write( "represents whatever you raise to the 1976th power to get \"%282a%2Bb%29%5E1976\". But can you just see what was raised to the 1976th power to get \"%282a%2Bb%29%5E1976\"?? Isn't it simply (2a+b)???

\n" ); document.write( "So at first look, \"root%281976%2C+%282a%2Bb%29%5E1976%29\" would seem to be 2a+b.

\n" ); document.write( "But as mentioned earlier, a 1976th root must never be negative. Could 2a+b be negative? Since we don't know what a or b are, we don't know. To ensure the \"non-negativeness\" of our answer we must use absolute value. So the correct answer is:
\n" ); document.write( "\"root%281976%2C+%282a%2Bb%29%5E1976%29+=+abs%282a%2Bb%29\"

\n" ); document.write( "P.S. Odd-numbered roots can be any number: positive, negative or zero. So never use absolute value on odd-numbered roots. For example:
\n" ); document.write( "\"root%285033%2C+%283x-9%29%5E5033%29+=+3x-9\"

\n" ); document.write( "P.P.S. You don't always need to use absolute values on even-numbered roots. If you know your answer cannot be negative then the absolute value is not needed. For example:
\n" ); document.write( "\"root%2840%2C+435%5E40%29+=+435\" (435 is obviously positive. No absolute value needed here.)
\n" ); document.write( "\"root%2832%2C+%28x%5E2%2B1%29%5E32%29+=+x%5E2+%2B+1\" (Although we don't know what x might be, we know that \"x%5E2\" will never be negative. And if \"x%5E2\" cannot be negative, then \"x%5E2%2B1\" cannot be negative either. So no absolute value is needed.) \n" ); document.write( "
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