Table of contents | |
What is a Cube? | |
What is a Cube Root? | |
The Cube Root Symbol | |
You Can Also Cube Negative Numbers | |
Perfect Cubes | |
Examples |
Cubes and cube roots often appear in various real-world contexts, from calculating the volume of objects to understanding growth patterns and exponential increases. For example, determining the volume of a box or calculating a growth rate over time relies on these principles.
In GMAT, mastering cubes and cube roots can provide you with quick shortcuts and insights to solve problems involving large numbers, measurements, and mathematical operations.
Have a look at this:
When we cube +5 we get +125: +5 × +5 × +5 = +125
When we cube −5 we get −125: −5 × −5 × −5 = −125
So the cube root of −125 is −5
The Perfect Cubes are the cubes of the whole numbers
It is easy to work out the cube root of a perfect cube, but it is really hard to work out other cube roots.
Example 1: If and are positive integers such that and , find the values of and
Sol: We are given Start by checking possible integer values of and :
For and would give .
So, +0=1000, which works.
Therefore, the solution is x=10 and y=0.Answer: Option 1
Example 2: A rectangular solid has a volume of 216 cubic inches. If the length of each edge is increased by 50%, what will be the new volume of the solid?
a. 324 cubic inches
b. 486 cubic inches
c. 512 cubic inches
d. 648 cubic inches
Sol: The volume of a rectangular solid is the product of its length, width, and height. If the edge length is increased by 50%, the new edge length is 1.5 times the original.
If the original volume is V=216 cubic inches, the new volume will be
115 videos|106 docs|113 tests
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1. What is a cube in mathematics? |
2. How do you calculate the cube root of a number? |
3. Can you cube negative numbers, and what is the result? |
4. What are perfect cubes, and can you provide examples? |
5. What is the significance of the cube root symbol, and how is it used? |
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