Question

Find each root, if possible. $$\sqrt[6]{-64}$$

   Find each root, if possible.
$$\sqrt[6]{-64}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 10, Problem 65

Instant Answer

Solved by Expert Ernest Castorena

06/26/2020

Step 1

This means we are looking for a number that, when raised to the power of 6, gives -64. Show more…

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Find each root, if possible. $$\sqrt[6]{-64}$$

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Key Concepts

Principal Square Root

The principal square root of a number is defined as the nonnegative value that, when squared, gives the original number. For example, ?64 equals 8 because 8² = 64, meaning that the radical symbol denotes the positive square root by convention.

Order of Operations with Radicals

When evaluating expressions involving radicals along with other operations, it is essential to follow the order of operations. In an expression such as -?64, the square root is calculated first, yielding 8, and then the negative sign is applied, resulting in -8.

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