Question
5:22 LTE 574 Take Quiz Exit Question 5 1 pts What is the \( \sqrt[3]{1000} \) ? 100 3000 10 30 Question 6 1 pts Solve the equation for \( p \). \[ p^{2}=36 \] \( p=6 \) \( p=9 \) \( p=72 \) \( p=18 \)
Ask by Reese Tucker. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**Question 5:** The cube root of 1000 is **10**.
**Question 6:** The solution to \( p^{2} = 36 \) is **\( p = 6 \)**.
Solution
Sure, let's go through each question one by one.
---
**Question 5**
*What is the \( \sqrt[3]{1000} \)?*
**Options:**
- 100
- 3000
- 10
- 30
**Solution:**
To find the cube root of 1000, you're looking for a number that, when multiplied by itself three times, equals 1000.
\[
\sqrt[3]{1000} = x \quad \text{such that} \quad x \times x \times x = 1000
\]
Since \(10 \times 10 \times 10 = 1000\),
**Answer:** **10**
---
**Question 6**
*Solve the equation for \( p \).*
\[
p^{2}=36
\]
**Options:**
- \( p=6 \)
- \( p=9 \)
- \( p=72 \)
- \( p=18 \)
**Solution:**
To solve for \( p \), take the square root of both sides of the equation.
\[
p = \sqrt{36} \quad \text{which gives} \quad p = \pm6
\]
However, among the provided options, only \( p = 6 \) is listed.
**Answer:** **\( p = 6 \)**
---
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Simplify this solution The Deep Dive
Did you know that the cube root of a number, like \( \sqrt[3]{1000} \), asks you what number multiplied by itself three times gives you that number? In this case, since \( 10 \times 10 \times 10 = 1000 \), the answer is 10! So, next time you're cube rooting, remember it's all about that three-fold multiplication! When you solve the equation \( p^{2}=36 \), you need to take the square root of both sides. This means you're looking for two potential values for \( p \): positive and negative! So in this case, \( p = 6 \) or \( p = -6 \), which means \( p \) could be either 6 or -6! It's like finding hidden treasures; you always have to consider all possible options!
