Question

Find all square roots of each number. $$81$$

   Find all square roots of each number.
$$81$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 10, Problem 10

Instant Answer

Solved by Expert Ernest Castorena

06/26/2020

Step 1

The square root of a number is a value that, when multiplied by itself, gives the original number. So, we need to find a number that, when multiplied by itself, equals 81. Show more…

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Find all square roots of each number. $$81$$

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Key Concepts

Square Roots

Square roots are numbers that, when multiplied by themselves, equal the original number. This concept is fundamental in algebra and is used to reverse the squaring process. When finding square roots in equations, both the positive and negative numbers are usually considered since both yield the same result when squared.

Principal Square Root

The principal square root of a nonnegative number is the nonnegative value that, when squared, equals the original number. It is the default value assigned when using the radical symbol, but it is important to note that the complete set of square roots of an equation typically includes both the principal (positive) and the negative counterpart.

Quadratic Equations

Quadratic equations of the form x² = c often have two solutions because squaring is not a one-to-one operation. Understanding this property is crucial for identifying all possible square roots of a number, as both the positive and negative values satisfy the original equation.

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