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5.5 roots of real numbers

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5.5 roots of real numbers

1. 1. 5.5 Roots of Real5.5 Roots of Real NumbersNumbers
2. 2. n b index radicand radical sign Note: square root when index is not visible
3. 3. Square RootSquare Root valuevalue squaresquare squaresquare rootroot 55 (5)(5)22 = 25= 25 -3-3 (-3)(-3)22 = 9= 9 25 5= 9 3= −  The inverse of squaring a valueThe inverse of squaring a value
4. 4. The nThe nthth rootroot if , thenn n a b b a= = valuevalue nnthth powerpower nnthth rootroot 33 (3)(3)33 = 27= 27 -2-2 (-2)(-2)55 = -32= -32 3 27 3= 5 32 2− = −
5. 5. Principal RootPrincipal Root valuevalue nnthth rootroot principalprincipal rootroot 6 3−  When there is more than 1 real root,When there is more than 1 real root, the nonnegative rootthe nonnegative root 36 3 27− 3− 6±
6. 6. The nThe nthth rootroot if , thenn n a b b a= = nn eveneven -------------------- oddodd -------------------- eithereither ------------------ -------------------- 1+ and 1- root 49 7= ± b is neg.(-)b is pos.(+) b is 0 no real root 25− 3 1 + root 8 2= 5 1- root 32 2− = − n 1real root 0 0=
7. 7.  ensures a nonnegative resultensures a nonnegative result 2 1 ( 5) ( 5) 5− = − = ** : ( ) ( )nNote even power odd power= 6 3 ( 2) ( 2) 8 8− = − = − =