Problem 2 Solve. $\sqrt[3]{-27}$... [FREE SOLUTION]

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Painless Algebra

Lynette Long

$Math Studyset 91影视 Explanations$ Math

2 Edition

Chapter 8: Problem 2

Solve. $\sqrt[3]{-27}$

Short Answer

Expert verified

The cube root of -27 is -3.

Step by step solution

Identify the Expression

The given expression is $\text{\textbackslash sqrt[3]\textbraceleft-27\textbraceright}$, which represents finding the cube root of 鈥�27.

Understand Cube Roots

Remember that the cube root of a number $a$ is a number $b$ such that $b^3 = a$.

Calculate the Cube Root

Find a number that when multiplied by itself three times equals -27. Notice that $-3 \times -3 \times -3 = -27$.

Verify the Solution

Verify that $(-3)^3 = -27$ to ensure the calculation is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Cube Roots

To solve cube roots, you need to find a number that, when multiplied by itself three times, gives you the original number. For example, to solve $\text{\textbackslash sqrt[3]\textbraceleft-27\textbraceright}$, you're looking for a number that satisfies $b^3 = -27$. Start by breaking down -27.
An easy way to approach this is to think of common cube numbers. The numbers $8, 27, 64$ and their negative counterparts are helpful when dealing with cube roots. If you guess $-3$, then test it:
$-3 \times -3 \times -3 = -27$. Since this is true, $-3$ is the correct cube root of $-27$.
Once you find the right number, always verify your solution to ensure correctness.

Negative Numbers

Negative numbers can be tricky, but it's important not to be intimidated by them. When dealing with negative numbers in cube roots, remember that the cube of a negative number is still negative. This is different from square roots where a negative number inside the square root leads to an imaginary number.
For example, $-3 \times -3 = 9$ and $+9 \times -3 = -27$. Here, the first multiplication flips the sign to positive, while the second multiplication flips it back to negative.
This is why the cube of any negative number remains negative. Understanding this will help you solve cube roots involving negative numbers with confidence.

Verifying Solutions

It's always good practice to verify your solutions. Once you've found the cube root, make sure to check your work. For instance, after determining that the cube root of $-27$ is $-3$, take a moment to verify it:
$(-3)^3 = -3 \times -3 \times -3 = -27$. Since the equation holds true, your solution is verified.
Verification helps ensure you haven't made any errors and confirms your understanding of the process. Always take the extra step to verify; it builds confidence in your math skills!

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91影视

Solve. \(\sqrt[3]{-27}\)

Short Answer

Step by step solution

Identify the Expression

Understand Cube Roots

Calculate the Cube Root

Verify the Solution

Key Concepts

Solving Cube Roots

Negative Numbers

Verifying Solutions

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