https://file.aiquickdraw.com/mathbot/file/172883672603537ylmuwf.jpg

Let's evaluate each of the expressions based on the image:

### (a) \(\sqrt[3]{27}\)
The cube root of 27 is the number that, when cubed, gives 27.
\[
\sqrt[3]{27} = 3 \quad \text{(since \(3^3 = 27\))}.
\]

### (b) \(-\sqrt{64}\)
The square root of 64 is 8, and applying the negative sign:
\[
-\sqrt{64} = -8.
\]

### (c) \(\sqrt[3]{8}\)
The cube root of 8 is the number that, when cubed, gives 8.
\[
\sqrt[3]{8} = 2 \quad \text{(since \(2^3 = 8\))}.
\]

### (d) \(\sqrt[3]{-216}\)
The cube root of -216 is the number that, when cubed, gives -216.
\[
\sqrt[3]{-216} = -6 \quad \text{(since \((-6)^3 = -216\))}.
\]

#### Summary of Answers:
- (a) \( \sqrt[3]{27} = 3 \)
- (b) \( -\sqrt{64} = -8 \)
- (c) \( \sqrt[3]{8} = 2 \)
- (d) \( \sqrt[3]{-216} = -6 \)

Would you like further details on any part of this solution?

### Here are five related questions for practice:
1. What is the cube root of 125?
2. Calculate \( \sqrt[3]{-125} \).
3. Find \( \sqrt[4]{16} \).
4. Simplify \( -\sqrt{144} \).
5. Evaluate \( \sqrt[3]{-27} \).

### Tip:
For cube roots, remember that they work for both positive and negative numbers, unlike square roots, which are only defined for non-negative numbers (unless using imaginary numbers).

Evaluate each of the following: (a) ∛27 (b) -√64 (c) ∛8 (d) ∛-216

Learn how to evaluate cube roots and square roots with step-by-step solutions to problems like ∛27, -√64, ∛8, and ∛-216. Understand the key properties of real numbers and roots, suitable for students in Grades 7-9.

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