https://file.aiquickdraw.com/mathbot/file/1729944726465ssha5mm6.jpg

To solve the problem, let’s break down each part of the question.

We are given the values:
- \( x_1 = 3 \times \sqrt{81} \)
- \( x_2 = 27 \)
- \( x_3 = 64 \)
- \( x_4 = 125 \)
- \( x_5 = 8 \)

The expression to simplify is:
\[
\sum_{i=2}^{4} x_i^{\frac{1}{3}}
\]
This means we need to find the cube root of each \( x_i \) from \( i=2 \) to \( i=4 \) and then sum those values.

### Step 1: Calculate \( x_1 \)
Since \( x_1 = 3 \times \sqrt{81} \):
\[
\sqrt{81} = 9, \quad \Rightarrow x_1 = 3 \times 9 = 27
\]

### Step 2: Calculate \( x_i^{\frac{1}{3}} \) for \( i=2 \) to \( i=4 \)
1. **For \( x_2 = 27 \):**
   \[
   x_2^{\frac{1}{3}} = \sqrt[3]{27} = 3
   \]

2. **For \( x_3 = 64 \):**
   \[
   x_3^{\frac{1}{3}} = \sqrt[3]{64} = 4
   \]

3. **For \( x_4 = 125 \):**
   \[
   x_4^{\frac{1}{3}} = \sqrt[3]{125} = 5
   \]

### Step 3: Sum the results
Now, add the results from \( x_2 \), \( x_3 \), and \( x_4 \):
\[
x_2^{\frac{1}{3}} + x_3^{\frac{1}{3}} + x_4^{\frac{1}{3}} = 3 + 4 + 5 = 12
\]

### Answer
The correct answer is:
\[
\text{c. } 12
\]

Would you like further details or explanations on any part of the solution? 

### Related Questions:
1. What is the cube root of a negative number?
2. How do you simplify expressions involving summations?
3. How do you calculate square roots and cube roots quickly?
4. What other methods can be used to simplify summations with roots?
5. Can this approach be extended to higher-order roots?

### Tip:
When calculating roots, it's often useful to remember the cube roots of common perfect cubes like 8, 27, 64, and 125.

Suppose that x1 = 3 * √81, x2 = 27, x3 = 64, x4 = 125 and x5 = 8. Simplifying Σ(i=2 to 4) xi^(1/3) gives which of the following values: 15, 14, 12, or 17?

Learn how to calculate the summation of cube roots for given values x2 = 27, x3 = 64, and x4 = 125, simplifying the expression Σ(i=2 to 4) xi^(1/3). This problem covers summation notation and cube root calculations, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation