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Chapter 10 Radicals and Rational Exponents

10.1 Finding Roots 10.2 Rational Exponents 10.3 Simplifying Expressions Containing Square Roots 10.4Simplifying Expressions Containing Higher Roots 10.5Adding, Subtracting, and Multiplying Radicals 10.6Dividing Radicals Putting it All Together 10.7Solving Radical Equations 10.8Complex Numbers 10 Radicals and Rational Exponents

Finding Roots 10.1 Find Square Roots and Principal Square Roots There are two questions that you can ask yourself to help you find the square root of a number. 1. What number do I square to get 36? 2. What number multiplied by itself equals 36? Ask yourself any of the two questions above to help you find the square root of a number.

Example 1 Find all square roots of 36. Solution Example 2 Find all square roots of 49. Solution

Be Careful Radical Sign Radical Radicand Radical Sign Radical Radicand

Example 3 Find each square root, if possible. Solution

It is necessary to estimate their places on a number line or on a Cartesian coordinate system when graphing. For the purpose of graphing, approximating a radical to the nearest tenth is sufficient. A calculator with key will give a better approximation of the radical.

Approximate the Square Root of a Whole Number Example 4 Solution What is the largest perfect square that is less than 17? What is the smallest perfect square that is greater than 17? Since 17 is between 16 and 25 (16 < 17 < 25), it is true that is between and

Find Higher Roots Example 5 Find each root. Solution Finding the cube root of a number is the opposite, or inverse procedure, of cubing a number. Finding the fourth root of a number and raising a number to the fourth power are Opposite, or inverse, procedures

Index Radicand Radical

Be Careful The table below contains powers of numbers that you are expected to know. Knowing these powers is necessary for finding roots.

Example 6 Find each root, if possible. Solution

Evaluate

Example 7 Simplify. Solution When the index is even, use the absolute value symbol to be certain that the result is not negative. When the index is even, use the absolute value symbol to be certain that the result is not negative. The index is odd, so the absolute value symbol is not necessary. The index is odd, so the absolute value symbol is not necessary. Odd index: the absolute value symbol is not necessary.