R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the...
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Transcript of R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the...
![Page 1: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/1.jpg)
R8 Radicals and Rational Exponents
![Page 2: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/2.jpg)
Radical Notation
n is called the index number
a is called the radicand
![Page 3: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/3.jpg)
Properties of Radicals
![Page 4: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/4.jpg)
Simplifying Radicals
1.The radicand has no factor raised to a power greater than or equal to the index number.
2.The radicand has no fractions.
3.No denominator contains a radical.
4.Exponents in the radicand and the index of the radical have no common factor.
5.All indicated operations have been performed
![Page 5: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/5.jpg)
• If there is no index #, it is understood to be 2
• When simplifying radicals use perfect squares, cubes, etc.
• Use factor trees to break a number into its prime factors
• Apply the properties of radicals and exponents
Simplifying Radicals
![Page 6: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/6.jpg)
Simplifying Radicals
![Page 7: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/7.jpg)
Simplify each radical expression
![Page 8: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/8.jpg)
Assume that all variables represent nonnegative real
numbers.
![Page 9: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/9.jpg)
Assume that all variables represent nonnegative real
numbers.
![Page 10: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/10.jpg)
Rewrite each of the following as a single number under the
radical sign.
![Page 11: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/11.jpg)
Multiplying Radicals
1.Radicals must have the same index number
2.Multiply outsides and insides together
3.Add exponents when multiplying
4.Simplify your expression
5.Combine all like terms
![Page 12: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/12.jpg)
Assume that all variables represent nonnegative real
numbers.
![Page 13: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/13.jpg)
Assume that all variables represent nonnegative real
numbers.
![Page 14: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/14.jpg)
Add/Subtract Radicals
1.Simplify each radical expression
2.Radicals must have the same index number and same radicand
3.Add the outside numbers together and the radicand remains the same
![Page 15: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/15.jpg)
Simplify each of the following radicals.
![Page 16: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/16.jpg)
Simplify each of the following radicals.
![Page 17: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/17.jpg)
Dividing Radicals1.No radicals in the
denominator
2.No fractions under the radicand
3.Apply the properties of radicals and exponents
![Page 18: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/18.jpg)
Assume that all variables represent nonnegative real
numbers and that no denominators are zero.
![Page 19: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/19.jpg)
Assume that all variables represent nonnegative real
numbers and that no denominators are zero.
![Page 20: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/20.jpg)
Assume that all variables represent nonnegative real
numbers and that no denominators are zero.
![Page 21: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/21.jpg)
Assume that all variables represent nonnegative real
numbers and that no denominators are zero.
![Page 22: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/22.jpg)
Simplify each of the following radicals.
![Page 23: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/23.jpg)
Rational Exponents
![Page 24: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/24.jpg)
Rational Exponents
![Page 25: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/25.jpg)
Simplify each expression containing fractional exponents
as radicals.
![Page 26: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/26.jpg)
Simplify each expression using radicals and exponents.
![Page 27: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/27.jpg)
Simplify each expression using radicals or exponents.
![Page 28: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/28.jpg)
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the
variables are positive.
![Page 29: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/29.jpg)
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the
variables are positive.
![Page 30: R8 Radicals and Rational Exponent s. Radical Notation n is called the index number a is called the radicand.](https://reader033.fdocuments.in/reader033/viewer/2022061616/56649ee55503460f94bf41a0/html5/thumbnails/30.jpg)
Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the
variables are positive.