Square Roots and Radicals 10

In "Square Roots and Radicals 10," we learn about higher order roots, including roots of negative numbers. If n is an even integer, the nth root of b to the n equals the absolute value of b. If n is an odd integer, the nth root of b to the n is b. The lesson also covers when to use absolute value signs in roots of negative numbers and how to simplify problems that are not perfect squares or cubes. It is important to note that if the variables represent positive numbers, we do not need to use absolute value signs.

Part 10 of Square Roots and Radicals covers higher order roots including roots of negative numbers.

• Why does the nth root of b^n equal |b| if n is even?
• Why do you have to use absolute value signs when finding roots of variables?
• Why is the fourth root of m^4 equal to |m|?
• What is the cube root of -8?
• What is the fourth root of (-2)^4?
• Why is the even root of a negative number not a real number?
• Why can you take an odd root of a negative number but not an even root?
• How do you simplify the cube root of -250x^6y^10?
• How do you simplify the square root of 45x^3y^9 if variables can be positive or negative?