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Look at this equation: \[ v^{3}=1000 \] What is \( v \), the cube root of 1,000 ? \[ v=10 \]

Ask by Rose Cox. in the United States
Mar 13,2025

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\( v = 10 \)

Solución

Let's solve the equation step by step to find the value of \( v \). 1. We start with the equation: \[ v^{3} = 1000 \] 2. To find \( v \), we need to take the cube root of both sides of the equation. This can be expressed mathematically as: \[ v = \sqrt[3]{1000} \] 3. Now, we can calculate the cube root of 1000. We know that: \[ 10 \times 10 \times 10 = 1000 \] Therefore, the cube root of 1000 is indeed 10. Thus, we conclude that: \[ v = 10 \] Your answer is correct! \( v \) is indeed 10.

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Beyond the Answer

Did you know that cube roots have been studied for centuries? The ancient Babylonians already had methods to approximate cube roots over 4,000 years ago! They used a blend of geometric intuitions and iterative calculations, which would eventually lay down the groundwork for modern algebra. They tackled numbers much larger than 1,000 with curiosity and ingenuity, shaping how we understand powers and roots today! In everyday life, cube roots pop up more often than you think! For example, if you're considering how much space you need to store a cubic item (like a box or shipment), knowing how to find the cube root helps quickly determine the side length. So, if you've got a volume of 1,000 cubic units, calculating the cube root shows that you'd need a side length of 10 units for a perfect cubic space. That’s handy when packing efficiently!

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