Evaluate the roots without using a calculator. Identify those that are not real numbers. √(0.64)

Name: Problem 16, Chapter 10: Beginning and Intermediate Algebra
Uploaded: 2021-03-24T15:15:58-08:00
Duration: 2 min 32 s
Channel: Noah Musser
Description: Evaluate the roots without using a calculator. Identify those that are not real numbers. √(0.64)

step 1 Hey there, we are doing number 16. Evaluate the roots without using a calculator. Okay, let's ta

Evaluate the roots without using a calculator. Identify...

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Key Concepts

Radicand Simplification

Simplifying the radicand, which is the quantity under the square root, involves techniques such as converting decimals to fractions or recognizing perfect squares. This simplification can make it easier to evaluate the square root exactly without the need for a calculator.

Square Root Function

The square root function assigns to a nonnegative number another number which, when squared, equals the original number. In the context of real numbers, only nonnegative values have real square roots, while square roots of negative numbers require extension to the complex number system.

Real Numbers

Real numbers include all the numbers on the number line—both rational and irrational numbers. When evaluating square roots, a positive radicand yields a real result, whereas a negative radicand does not have a real square root.

Complex Numbers

Complex numbers extend the real number system to include numbers involving the imaginary unit 'i', where i is defined as the square root of -1. This concept becomes crucial when evaluating square roots of negative numbers, as such roots are not real but instead form complex numbers.

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