Find each root. √((81)/(16))

Name: Problem 38, Chapter 7: Algebra for College Students
Uploaded: 2022-02-15T18:26:27-08:00
Duration: 2 min
Channel: Dheeraj
Description: Find each root. √((81)/(16))

Key Concepts

Rational Exponent Representation

This concept involves rewriting radicals as expressions with fractional exponents, which simplifies the manipulation and evaluation of roots. For example, expressing a number raised to the 1/n power allows us to apply the rules of exponents and factorization, especially when the radicand can be represented as a power of a smaller number.

Nth Roots

The concept of nth roots extends the idea of square roots to any positive integer n. This involves finding all numbers that, when raised to the nth power, produce the original number. In the context of complex numbers, an nth degree equation has exactly n distinct roots, which may include both real and non-real (complex) solutions.

Polar Form

Converting numbers into polar form is essential when finding roots of complex numbers. In polar form, a complex number is represented by its magnitude and angle, facilitating the application of trigonometric methods. This is particularly useful in simplifying the computation of all nth roots using angle division.

De Moivre's Theorem

De Moivre's Theorem connects complex numbers in polar form with exponentiation, providing a formula to compute powers and roots of complex numbers. It states that raising a complex number to the power n multiplies its angle by n while raising its magnitude to the power n, and conversely, the nth root divides the angle by n, allowing for the systematic computation of all possible roots.

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